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The Browns are being sued by their city.
Cleveland leadership filed legislation on Tuesday to prevent the team from moving.
City officials are invoking the "Modell Law" which was passed back in 1996 after former owner Art Modell relocated the franchise to Baltimore.
Current owners Jimmy and Dee Haslam have expressed interest in building a new domed stadium in Brook Park, which is about 10 miles south of Cleveland.
The project would cost nearly two-and-a-half billion dollars.
The team's current lease at Huntington Bank Stadium expires after the 2028 season.