The Titans are signing Rudolph to a one-year, $3.6 million contract Wednesday, Turron Davenport of ESPN.com reports.
Rudolph has free-agent interest from multiple teams, according to Mike Garafolo of NFL Network.
GM Omar Khan said Thursday that Rudolph knows the Steelers want to re-sign him, Mark Kaboly of The Athletic reports.
Rudolph and the Steelers will play their wild-card matchup against the Bills on Monday at 4:30 p.m. ET after the game was postponed Saturday due to extreme weather conditions.
Steelers head coach Mike Tomlin confirmed Tuesday that Rudolph will remain the team's starting quarterback for Sunday's wild-card game in Buffalo, Mike DeFabo of The Athletic reports.
Rudolph is set to start Saturday's game against the Ravens, Missi Matthews of the Steelers' official site reports.
Rudolph is slated to start Sunday's game against the Seahawks, Ian Rapoport of NFL Network and Alan Saunders of SteelersNow.com report.
Head coach Mike Tomlin said Tuesday that Rudolph is "scheduled to be" the team's starting quarterback for Sunday's game in Seattle, Brooke Pryor of ESPN.com reports.
Rudolph will start at quarterback Saturday against the Bengals, Brooke Pryor of ESPN.com reports.
Coach Mike Tomlin said Monday that the Steelers are currently planning for Rudolph to start Saturday's divisional matchup against the Bengals, though Kenny Pickett (ankle) hasn't been ruled out, Teresa Varley of the Steelers' official site reports.