The 26-year-old is currently out of favour at Serie A side Juventus after suffering a knee injury in January.
He made 83 appearances for Liverpool and is thought to be keen on a move back to the Premier League, while Stoke boss Tony Pulis has admitted the need for new signings at the Britannia Stadium.
"It is no secret that we need to bring players in to boost the squad," Pulis said. "We are hoping to do some deals over the next few weeks."
Both Paris Saint-Germain and Marseille are thought to be interested in Sissoko, who joined the Turin outfit in 2008 in a deal worth around £8m.