Chalme, 32, was initially a regular after joining Bordeaux from Lille in 2007 and helped the club to the Ligue 1 and Coupe de la Ligue trophies in 2009.
However, the defender has made only one Ligue 1 appearance for Bordeaux this season and his parent club have confirmed he will spend the remainder of the campaign at the team sitting 16th in the table.
Ajaccio are also close to signing Auxerre striker Oliech, according to widespread reports.
Oliech has scored three goals in 17 games in Ligue 2 this season but appears poised to return to the top flight.
The 27-year-old signed for Nantes in 2005 before moving to Auxerre two years later.