The state is seeking to relocate more than 400 detainees from a jail in East Cambridge to the Middlesex House of Correction in Billerica because of the deteriorating conditions at the facility.

The Executive Office for ­Administration and Finance has allocated $37 million for construction of two new wings at the Billerica facility, one containing 256 beds in double-bunk cells and another containing 240 beds divided among four open, barracks-style rooms.