The Potters had the Moroccan on loan last season and the winger impressed with some eye-catching displays as he netted four goals 19 appearances including a memorable winner against Chelsea in a 3-2 victory in December.
The teams had been in discussions about a permanent switch and reportedly reached an agreement in mid-July.
Reports earlier this year suggested that the Reds were looking for around £7 million for the 25-year-old, although it was believed that the eventual fee was closer to around £4.5 million.
However, Hughes has since stated that the talks had "gone cold" and indicated that he was looking elsewhere should the deal break down before the end of the transfer window.
He told Stoke's official website: “It’s common knowledge that Ozzie is somebody that we would like to bring into the club, but at the moment that deal has gone cold.
“He is one that we have chased for a while now but there hasn’t been any real movement on that front, so we will just have to wait and see what the situation is with regards to that deal.
“There are plenty of options available to me and I am really pleased with the business we have been able to conclude so far. We are in a really good place at this moment in time.
“We would like to bring one more player into the club, but he has got to be of the right quality because as we saw [against Betis], we have a squad of players with real strength in depth.”
After their best-ever Premier League finish of ninth last term, Hughes has so far added to his side with the signings of Mame Biram Diouf, Phil Bardsley, Peter Skapetis, Dionatan Teixera and ex-Barcelona starlet Bojan.
It is the arrival of the former Barca forward that has excited fans at the Britannia this summer, and the striker has netted three goals in as many pre-season games, including a memorable strike against Real Betis on Wednesday evening.
Bojan was instrumental throughout as Hughes' side recorded a 2-0 win over the La Liga side and he was eventually given a standing ovation after he was withdrawn for Peter Crouch late on.
Stoke entertain Aston Villa on the opening day of the new Premier League season.