Bastia were very keen on signing the journeyman forward as he is out-of-favour at Rennes.
Vairelles admitted he would have jumped at the chance to return to Bastia as he wants to be playing regularly.
"I had real trails, notably with Bastia. I am living a strange situation here," said Vairelles.
"I hold on, but at my age I want to play.
"My family is living in Corsica and I would love that solution.
"It seems the Bastia coach didn't want me to rejoin them."
One player who is leaving Rennes for Bastia is Philippe Delaye after he cancelled his contract.
Delaye is set to sign a six-month deal with Bastia in the next few days.
