The 22-year-old has already admitted that he wants to stay in the Premier League next season, despite a largely disappointing campaign at Loftus Road.
Hoilett came close to leaving the club in January and is thought to be desperate to join a stable top-flight team to revive his career.
Everton and Stoke were both interested parties when Hoilett was available on a free transfer last season and want to make the Canadian forward an early summer acquisition, according to the Daily Mail.
Stoke boss Tony Pulis is thought to be desperate to sign a pacy winger to add impetus in the final third, while Everton manager David Moyes is reportedly a long-term admirer of the Hoops winger.
Hoilett has scored just one goal in 24 Premier League appearances for QPR so far this term.