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Where are Patriots headed in free agency?

Julian Edelman might cost the Patriots only $3 million-$4 million per season.

AP/File

Julian Edelman might cost the Patriots only $3 million-$4 million per season.

NFL free agency officially opens for business at 4 p.m. Tuesday, and a handful of the top free agents are expected to land major deals. Whether the Patriots will be involved in the bidding, however, remains to be seen.

The Patriots have two impact free agents of their own — receiver Julian Edelman and cornerback Aqib Talib. Of the two, Edelman appears to be the more likely to return, with Talib, perhaps the top cornerback available on the market, primed to cash in with a major deal worth $9 million-$10 million per season, with the Redskins reportedly hot on his trail. The Patriots have several holes to fill, have approximately $15 million in salary cap space as of Monday, and Edelman might cost them only $3 million-$4 million per season.

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But unless the Patriots decide to pony up big dough for Talib or the other top cornerback on the market, Titans four-year veteran Alterraun Verner, they likely will be looking for bargains in free agency instead of signing the most expensive players.

A handful of top free agents will likely sign contracts shortly after the new league year begins Tuesday afternoon, but like most years it probably won’t be a flurry of activity. While teams have been able to negotiate with free agents since Saturday, they can’t perform physicals and medical checks until Tuesday afternoon, which could delay the process for someone like Talib, who is coming off hip and knee injuries.

Verner, who is only 25 and has played in all 64 games of his NFL career, will compete with Talib for the top cornerback contract. Both are likely to better the contract recently signed by Miami’s Brent Grimes ($16 million guaranteed over two years). Verner has several teams interested in him, and said Monday on Sirius XM radio that Patriots safety Devin McCourty has tried to convince him to come to New England, though the Patriots may not be willing to pay that much for one player.

A handful of left tackles are also expected to play musical chairs and sign fairly quickly. The Dolphins reportedly are high on Kansas City’s Branden Albert, the Cardinals are eyeing Oakland’s Jared Veldheer, the Raiders want St. Louis’s Rodger Saffold, and the Ravens’ Eugene Monroe will be speaking with several teams, but might ultimately return to Baltimore.

Other top free agents who could sign quickly include Buffalo safety Jairus Byrd, four defensive ends — Minnesota’s Jared Allen, Cincinnati’s Michael Johnson, Oakland’s Lamarr Houston, Baltimore’s Arthur Jones — and Denver receiver Eric Decker. Quarterbacks Michael Vick and Josh McCown might also quickly find work, with Oakland, Buffalo, and the Jets looking like the best suitors for Vick, who still wants to be a starter. And one of the top pass rushers already came off the board, with Michael Bennett re-signing with Seattle on Monday for $16 million guaranteed over four years.

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A handful of teams are flush with salary cap space and will likely overpay a handful of free agents to meet minimum spending requirements — Oakland ($60 million under the cap), Jacksonville ($56 million), Cleveland ($49 million), Minnesota ($40 million), the Jets ($40 million), Indianapolis ($38 million), and Miami ($34 million).

The Patriots, though, appear to be more concerned with handling some of their own business first and looking for good bargains in free agency, of which there should be a handful.

Of most concerns are a contract extension or restructure for defensive tackle Vince Wilfork, who is set to make $7.5 million with a salary cap number of $11.6 million but is entering the last year of his contract and coming off an Achilles’ injury, and a $2 million guarantee for receiver Danny Amendola on Tuesday.

The Patriots would like to slash Wilfork’s salary cap number, and adding a couple extra years to his contract could help the two sides come to an agreement.

If not, the Patriots could cut Wilfork, 32, who didn’t play well last year before tearing his Achilles’ in Week 4.

Amendola, who underperformed last year and fell out of Tom Brady’s favor at the end of the season, has been rumored to be on the trade or cutting block, with his savings used to sign Edelman.

While the $2 million guarantee complicates matters, his contract has offset language that still gives the Patriots some flexibility if they decide to move on from their disappointing free agent signing from a year ago.

The Patriots have holes to fill at defensive line, cornerback, receiver, tight end, and interior offensive line.

A look at some of the players that might interest them:

 Cornerback Antonio Cromartie: If they decide that Talib and Verner are too expensive and can’t swing a trade for Tampa Bay’s Darrelle Revis, then Cromartie, the former Jets cornerback, could be a good, cheaper replacement. Cromartie, who turns 30 next month, is a big cornerback like Talib (6-2, 210) and has played in at least 15 games for the last six seasons before the Jets released him on Sunday. Denver’s Dominique Rodgers-Cromartie could also be a decent option, though he doesn’t have the size of Talib or Cromartie.

 Receivers Steve Smith, Hakeem Nicks, and Santonio Holmes. Nicks, the Giants’ 2009 first-round pick, has 27 touchdowns in five seasons but had zero last year and could be a good one-year rental for a team like the Patriots needing to improve their receiver corps. Smith is being shopped by the Panthers and may be released after 13 seasons with the team, according to NFL Network. Though he is only 5-9 and will turn 35 this offseason, Smith is still a physical receiver who could be another low-cost option. And Holmes hasn’t been healthy since 2011, but was released by the Jets on Monday.

 Defensive ends Jason Babin, Antonio Smith, and Allen. Allen, who had double-digit sacks for the last seven seasons, would be a great fit for the Patriots if he wants to chase a championship ring, but he might be a bit out of their price range. Smith, 32, and Babin, 33, could be good, cheap veteran options to help take the pressure off Rob Ninkovich and Chandler Jones.

 Tight ends Dustin Keller, Jermichael Finley, Scott Chandler. The Patriots need to find another tight end as insurance for oft-injured Rob Gronkowski. While the tight end market is light in free agency, these three could provide good value, although Keller (ACL) and Finley (neck) are coming off significant injuries and would be no sure bet to stay healthy.

Ben Volin can be reached at ben.volin@globe.com. Follow him on Twitter @BenVolin.

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