The Morocco winger spent the season on loan at the Britannia Stadium from the Anfield outfit, making 25 appearances in all competitions and scoring five goals.
Hughes is keen to retain the services of the 25-year-old, despite expectations that Liverpool's return to Europe's elite competition will require greater squad depth for Reds manager Brendan Rodgers.
The Stoke boss believes that the anticipated investment in new talent by Rodgers this summer will see Assaidi, who moved to Merseyside in a £2.4million deal from Heerenveen in August 2012, remain on the fringes of the first-team fold.
Hughes told The Sentinel: "The ball is very much in Liverpool's court because he is their player.
"I'm not saying I know what they are thinking, but I would imagine that being in the Champions League they will spend more money this summer.
"And that could go against Ossie having a place there.
"He is their player and we mustn't forget that, but yes we are hopeful of keeping him here.
"It's fair to say that he's enjoyed his time with us and we have enjoyed having him here."