The 27-year-old right back was named in Le Championnat's team of the season last year, but is unable to find an agreement with Auxerre over a new deal.
Radet is unhappy that he has not been offered a good enough package and will be thinking about leave Guy Roux's side.
"This proposition of two additional years is not interesting," said Radet. "I am a 27-year-old, and I need to earn my living.
"It is not the case at Auxerre. Compared to other players, I don't have what I deserve. I regret the club's poor consideration of my qualities.
"If you are listening to the officials, it seems you will ruin the club. But I will give myself another chance to sign here again.
"I am not obsessed by a departure. My wife would like to stay in France."
Premiership sides Fulham and Arsenal are said to be interested in Radet should he join the mass ranks of departures from Auxerre in the summer.
Olivier Kapo, Jean-Alain Boumsong, Djibril Cisse and Philippe Mexes are all heading out of Stadde Abbe-Deschamps, and Radet's departure with be another blow.
On possible replacements, Roux is thought to be eyeing Montpellier's Habib Bamogo and Liverpool's young striker Florent Sinama-Pongolle.
