The former Doctor Who star is said to have held talks over Skype about appearing in the film with director Justin Lin, according to Latino Review.
Luke Evans is also rumoured to be in negotiations for the project, with reports suggesting that he has been offered the role of a villain. Details of the part Tennant is in contention for have not been disclosed.
Paul Walker, Michelle Rodriguez, Vin Diesel, Dwayne Johnson, Jordana Brewster and newcomer Gina Carano are tipped to star in The Fast and the Furious 6, which begins shooting in June.
Rihanna is also said to be in contention after studio executives approached her following her screen debut in Battleship.
The Fast and the Furious 6 is scheduled to arrive in cinemas on May 24, 2013.
Watch Dwayne Johnson talk about The Fast and the Furious 6 below: