The left-back is wanted by Bournemouth as a replacement for Milos Kerkez, with the Hungary international a step away from joining Liverpool.
The Sun says Aston Villa have also jumped into the battle to land Truffert.
Villa boss Unai Emery is said to be seeking a new left-back with Lucas Digne and Ian Maatsen failing to impress the Spaniard.
Rennes want £20m to sell 23-year-old Truffert this summer.