Terms of the offer sheet, confirmed by team sources, were not yet known.
The Green Bay Packers retained a right of first refusal to Bush by making him a one-year tender offer of $1.01 million last month. Green Bay has seven days to match or pass on the offer sheet. If the Packers match it, they keep Bush and assume the terms of the offer sheet. If they pass, Bush moves to Tennessee and the Packers receive no draft pick compensation, since Bush originally entered the league as an undrafted free agent.
Bush, 24, had been sought by several teams. A onetime waiver claim from Carolina in 2006, Bush has good size (6-foot-2, 200 pounds), can play cornerback or safety and is a special teams terror.
Bush started one of 47 games in three seasons, but the former Utah State standout can help a team in a lot of ways, including as a nickel back. He has double-digit special teams tackles in each of three seasons in the league, including 17 last season.
The Titans have only three experienced cornerbacks under contract. They already have lost unrestricted free agent Eric King. Unrestricted free agent cornerback Chris Carr, who is also the team's return man, reached an agreement in principle with the Baltimore Ravens on Saturday.
Len Pasquarelli is a senior NFL writer for ESPN.com.