The Moroccan spent last season on loan at Stoke, scoring five goals in 25 appearances, and manager Mark Hughes is hoping to bring him back to the Britannia Stadium.
Reports suggested that Liverpool’s original valuation was too high for the Potters, but they are thought to have agreed a fee in the region of £4.5m which could eventually rise to £7m.
Stoke were also linked with Norwich’s Nathan Redmond as they searched for new widemen following the departures of Matty Etherington, Jermaine Pennant and Michael Kightly.
Speaking earlier this month, Hughes said: "We are still looking. We have strengthened defensively, in midfield and up front, so the wide areas is somewhere we have to address, with letting Matty go and not knowing about Ossie.
"It's fair to say we have to look to try to bring a bit more strength into that area."
Assaidi could become Stoke's fifth summer signing following the arrivals of striker Mame Biram Diouf, midfielder Steve Sidwell, and defenders Phil Bardsley and Dionatan Teixeira.