The 25-year-old winger enjoyed a productive loan spell at the Britannia Stadium in 2013/14 and was quickly identified as a top summer target for Mark Hughes.
He has, however, struggled with knee problems in recent times and has seen his valuation soar and interest in his services rise on the back of a number of eye-catching displays.
A combination of those factors is making it increasingly difficult for Stoke to negotiate a deal that suits all parties, with chief executive Tony Scholes conceding that focus may have to be shifted elsewhere.
He told The Sentinel: “We’ve spoken to Liverpool about Oussama and we’ve spoken to his agent. 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.”
Were Stoke to abandon their efforts to land Assaidi, Scholes claims a number of alternative options have already been identified.
He said: “It’s important you don’t put all your eggs in one basket.
“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.”