The 29-year-old midfielder is club captain at Lille, but is looking for a new challenge after five years with the 2011 Ligue 1 champions.
He has previously taken in a spell in Spain with Villarreal, but returned to his native France after just one season.
Despite enduring a tough time in La Liga, Mavuba says he would welcome the opportunity to take on another foreign challenge.
The France international has been linked with a move to Everton and is ruling nothing out ahead of the summer transfer window.
"To be honest, I want to experience playing abroad again," said Mavuba.
"I have been abroad before with Villarreal in 2007. That did not work out how I had hoped, but I wasn't very experienced at that time. I am ready now."