Rangers have rejected the £3.75m bid from Bordeaux, as they also look to bring back Kyle Lafferty to the Ibrox.
The bid, which was submitted on Wednesday, was quickly rejected by Rangers bosses.
Rangers had previously received interest from Chinese side Beijing Renhe for Morelos in January.
Beijing Renhe were willing to pay around £8m for the player, but Rangers are unwilling to let him leave.
Morelos has scored in his last two appearances, and it will remain to be seen if Bordeaux will increase their offer to try and tempt a sale from Rangers.