Tony Scholes, Stoke chief executive, has conceded that the Staffordshire club are unlikely to be able to lure the 25-year-old back to the Britannia Stadium, where he spent last season on loan.
Manager Mark Hughes previously made clear his desire to keep Assaidi, who scored four goals in 19 Premier League appearances for Stoke.
However, Scholes has hinted that talks have stalled over a possible deal.
"We've spoken to Liverpool about Oussama and we've spoken to his agent," Scholes told the Stoke Sentinel.
"Sometimes deals look difficult to do and this one, if I'm frank, this is in the very difficult section. We'll see.
"He had a great season with us last year. We like him a lot, we know what he can bring to the club and he knows the club, that's an advantage.
"There is always a risk with any purchase of a player, but those are reduced substantially when you have had that player with you.
"It's a deal we would like to do, but we will have to wait and see."
Stoke have been the busiest Premier League club during the close-season so far, signing Phil Bardsley, Steve Sidwell and Mame Diouf.
And Scholes insists that Stoke will waste little time earmarking different transfer targets should their pursuit of Assaidi prove unsuccessful.
He added: "You have to make sure you are tracking a number of players for any particular position at any particular time.
"If one deal isn't possible you have another to go to."
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