The Moroccan spent last season on loan at the Britannia Stadium and the club remain hopeful of making the deal permanent.
Assaidi spent the season on loan at the Britannia Stadium last term after failing to make an impact at Anfield since his £2.4 million move from Heerenveen in 2012.
He made more of an impact for the Potters having scored in games against the likes of Chelsea, Newcastle United and Everton.
But the report says a move has stalled because of concerns over the Moroccan's fitness, and the price-tag, believed to be around £5 million, but Stoke boss Mark Hughes is said to still be keen on the player.
Last month the chief executive of Stoke City Tony Scholes said the price-tag was 'just wrong'.
He was quoted, saying: "He did very well last year and settled in. Everything points to it being a good match for both the club and the player.
"But, at the moment, the prices we are being quoted are just wrong."
Any proceeds from a sale for Liverpool is likely to be reinvested in the squad. Though Assaidi has had a couple of injury problems, the impact he has had at Stoke seems to make him a good option for the Potters, and if they do sign him, Mark Hughes will be hoping for a season relatively free from injury for the Moroccan.