The 24-year-old has been widely linked with a move to Europe after starring for his country in the 2013 Africa Cup of Nations.
And, having tabled an offer worth around €1 million, the Corsican side are set to see off competition from Toulouse, Auxerre and Ajaccio.
Mba left Nigeria on Sunday for France and confirmed that he is set to undergo a medical with the Armand Cesari outfit.
"I send my gratitude to Warri Wolves for giving me the permission to go for the medicals at Bastia," he told reporters.
"I pray that it will work well so that I can move to the next level in my career."
Mba has been on loan at Enugu Rangers from Warri Wolves in recent months.