ESPN's Adam Schefter reported that the Jaguars have had trade talks with other teams about Fournette, who gained 1,674 yards from scrimmage last season and is scheduled to make just $4.16 million in base salary this year.
But a source told Anderson on Monday morning that the Buccaneers feel there is plenty of depth at running back in this year's NFL draft.
Fournette, 25, rushed for a career-high 1,152 yards and caught a team-high 76 passes last season while scoring only three touchdowns. The Jaguars have until May 4 to exercise their fifth-year option on Fournette.
Running back has emerged as a position of need for the Buccaneers, who are expected to be a contender in the NFC after signing Tom Brady last month.
The Buccaneers own the 14th, 45th and 76th overall picks in the draft, which starts Thursday. ESPN's Mel Kiper Jr. projected that Tampa Bay will select Wisconsin running back Jonathan Taylor at No. 45 in his most recent mock draft.