Toure has been without a club since leaving China Super League outfit Qingdao Huanghai in January, despite being linked with a host of sides from across Europe, Asia and the Americas.
The 37-year-old is said to have approached Brest during the latest window, but was reportedly rejected by the club's sporting director Gregory Lorenzi over fears he might disrupt the dressing room.
"I spoke with people who saw this idea as interesting because it could make people talk about Brest. But I was wondering, facing my coach, if a player like that could be easy to handle in the dressing room.
"With regard to the other [squad] players, it could have been complicated so we preferred not to follow up."