Sen. Tom Coburn (R-Okla.) is working with Democratic senators on a bill that would mandate background checks for all gun buyers, with some limited exceptions.

In an interview Friday with a Tulsa television station, Coburn said he is working with Sens. Charles E. Schumer (D-N.Y.) and Joe Manchin III (D-W. Va.) on plans to keep weapons away from criminals and the mentally ill.

Coburn’s office didn’t immediately respond to requests for comment, but other Senate aides familiar with the negotiations confirmed his involvement. If a deal involving Coburn pans out, his ruby-red Republican reputation would lend significantly to any bipartisan effort to draft gun-control legislation.