The winger's ongoing knee problem, an unexpectedly high valuation and rival interest from top clubs around Europe are obstacles the Potters are unlikely to overcome.
Stoke chief Tony Scholes 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."
For the big stories and the banter follow us on Twitter: @tribalfootball