Tennessee is internally discussing a new contract for Tannehill after the 2019 campaign concludes, a source told ESPN's Dianna Russini.
The former first-round pick was traded to the Titans in March after seven seasons with the Miami Dolphins and is set to hit free agency in 2020.
Tennessee prefers to negotiate a deal for Tannehill to be the team's future starting quarterback rather than use the franchise tag, Russini adds.
The 31-year-old took over for Marcus Mariota in Week 7 and has amassed a 5-1 record since. He's completed nearly 72% of his passes for 12 touchdowns and three interceptions across six starts.
The Titans currently sit one spot behind an AFC wild-card berth, tied with the Pittsburgh Steelers at 7-5.