State planners say federal transit officials have signed off on an environmental impact study of the Green Line Extension, clearing an incremental hurdle for the project. Without the environmental thumbs-up, the project would lose a shot at $557 million in federal New Starts grants requested by the state and currently under final review by the Federal Transit Administration. In its application, the state’s Department of Transportation also previewed likely long-term options for funding mass transit costs. The options would require legislative action before the start of the next fiscal year. “The New Starts program is one of the most competitive funding programs in the nation, and MassDOT and the MBTA have spent four years preparing application materials,’’ the MBTA said in a prepared statement. “Preliminary approval under the New Starts program is a major step forward for the Green Line Extension project.’’ The menu of revenue possibilities includes suggestions of tying the state’s gas tax to inflation; boosting parking and vehicle registration fees; dedicating some gaming revenue to transportation costs; and taxing motorists 1 cent for every mile they drive.