Webster called the discussions "fairly substantial" but said no deal was imminent. Webster said the team was hoping to acquire draft picks rather than existing players.
Three of the teams Tennessee has spoken with are St. Louis, Cleveland and the New York Jets, according to the report. Ian Rapoport of NFL Network reports the Chicago Bears are also in contact with the Titans for the pick.
On Wednesday, Cleveland offered its No. 12 and No. 19 first-round picks to Tennessee in exchange for the No. 2 pick, according to ESPN. Tennessee is reportedly looking to acquire at least one top-16 pick in exchange for its No. 2 pick.
Acquiring Tennessee's pick has been the goal of several teams ostensibly looking to trade up in order to acquire former Oregon quarterback Marcus Mariota, who many believe will be drafted second.
Tennessee finished the 2014 season 2-14, tied for the worst record in the NFL.