The 31-year-old powerful right-back has also been linked with a potential move to Everton and Sunderland.
The France international has Champions League experience during his time at Lens and was strongly linked with a move to Newcastle and West Ham before signing a contract extension at Rennes in 2009.
Fanni, who has been at the Stade Velodrome since 2011, is reportedly keen on joining the Potters but Marseille are holding out for more money.
The player told skysports.com: "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."