Linebacker Matt Roth, claimed off waivers from Miami on Nov. 25, received a second-round tender from the Browns, ESPN's Adam Schefter reported on his Twitter page.
Roth started the final six games with the Browns and finished that stint with 28 tackles, four sacks and a fumble recovery.
Roth is a restricted free agent, along with several other key Browns veterans -- fullback Lawrence Vickers, running back Jerome Harrison, linebackers D'Qwell Jackson and Jason Trusnik and safeties Abram Elam and Brodney Pool.
If another team signed Roth and the Browns elected not to match, the Browns would receive a second-round pick in return.
Tender offers to restricted and unrestricted free agents are due by 4 p.m. today. Free agency and the NFL trading period begins at 12:01 a.m. Friday.