The 100,000-square-foot building at 83 Lockwood Ave., which at one point housed the Rogers Magnet Elementary School and later charter school Trailblazers Academy, is one of the places officials are examining as the home of a new public school, said Matt Quinones, the city’s director of operations. A school building master plan presented in February called for building or expanding four schools, including a potential new K-8 school in south Stamford. As part of the plan, four schools would shutter: Cloonan and Dolan middle schools, Toquam Magnet Elementary School and KT Murphy Elementary School. If approved, the city would be eligible for a reimbursement rate of 60 percent. Previously, Stamford received a 20 percent refund for school construction projects, but that was changed this week through special legislation on the state level.