The France international right-back is keen to a move to the Premier League, but his club have rejected a bid from the Potters as they hold out for a higher offer
The French international has been linked with a move to the Premier League for a number of years, with Everton and Sunderland also said to be interested.
The Potters have now made the first move, although the French club are said to be holding out for a higher offer.
The 31-year-old admits that he is keen to move to the Premier League, telling Sky Sports: "I have been linked with English clubs for the past three years, but I am still in France.
"Yes I want to play in England but I have a contract here, unless the two clubs agree a fee, it is not in my hands.
"I want to play in the top league and return in the French squad."
Fanni moved to the Stade Velodrome in early 2011, and has been an almost ever-present for Les Phoceens this season as they compete for the Champions League places in Ligue 1.