The Moroccan arrived at Anfield in 2012 as Brendan Rodgers' first signing, but the wide-man struggled to make an impact in his debut season, before he was shipped out to the Potters last term.
Legendary Liverpool defender Jamie Carragher famously branded his former teammate as a "Monday to Friday player" - meaning he would look the part in training until the weekend's game.
However, Assaidi's fortunes improved drastically at Stoke last term, where he made 19 appearances and scored four goals including a memorable winner against Chelsea in a 3-2 victory in December.
A delegation from Liverpool has been dispatched to discuss the terms of the switch with officials from the Potters, according to Sky Sports, although it is unclear if an agreement has so far been reached.
Reports earlier this year suggested that the Reds were looking for around £7 million for the 25-year-old, although The Telegraph has claimed that the fee is likely to be closer to around £4.5 million.
The report claims that the deal will be wrapped up within the next 48 hours and Assaidi will become Stoke's fifth signing of the summer.
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 and Dionatan Teixera.
Stoke entertain Aston Villa on the opening day of the new Premier League season next month.