Schefter noted Walker sat out in 2020 because of the COVID-19 pandemic and to get 100 percent healthy.
The 36-year-old Walker, who is a free agent, missed all but one game in 2018 with a dislocated ankle and played only seven games in 2019 because of another ankle injury.
Walker is a 14-year veteran who spent the first half of his career with the San Francisco 49ers and the second half with the Titans.
He was primarily a backup tight end and special teamer during his time with San Francisco, never recording more than 344 receiving yards in a season. After signing with the Titans in 2013, however, Walker became one of the best pass-catching tight ends in the NFL.
From 2014-17, Walker finished with at least 800 receiving yards each season and scored 20 touchdowns, and he was also named to the Pro Bowl three times.
His most productive season came in 2015 when he set career highs with 94 catches and 1,088 yards to go along with six touchdowns.
He was injured in Week 1 in 2018 and missed the last nine games of the 2019 campaign, finishing with 21 grabs for 215 yards and two touchdowns.
In 183 regular-season games, Walker has 504 receptions for 5,888 yards and 36 touchdowns. He has also made 16 catches for 244 yards in six playoff games over three seasons.
While it is unclear where Walker might land in free agency, a return to Tennessee is not out of the question since incumbent starter Jonnu Smith will be a free agent.
If Smith signs elsewhere, Walker could pair with Anthony Firkser, who is set for restricted free agency.
Signing Walker as a No. 1 tight end would be a risk given his age and the fact he hasn't played much over the past three years, but his resume is impressive enough that some team figures to give him an opportunity.