According to the Telegraph, representatives of McCarthy have told the Potters that he is interested in succeeding Paul Lambert at the bet365 Stadium, after the Scot recently departed the club via mutual consent.
McCarthy himself has been without a club since leaving Portman Road at the beginning of April in somewhat acrimonious circumstances after six years at the club, and is now believed to be ready to make a return back to management, citing Stoke as a possible destination.
The 59-year-old offers a wealth of experience in the role, managing the Republic of Ireland at the 2002 World Cup and Premier League campaigns with Sunderland and Wolves among his list of achievements, as Stoke now look to rebuild after what was a dismal campaign.
Finishing 19th in the Premier League, Lambert came in to replace Mark Hughes in January with the club in 18th, although a run of two wins out of a possible 15 meant Stoke were resigned to the reality of relegation, and will compete in their first Championship season since 2008.
Should McCarthy be appointed as Stoke's new manager, he will have the arduous task of assembling a side that will no doubt be void of some of their high profile stars come the start of next season.
The likes of Jack Butland and Joe Allen are expected to leave for pastures new, while Xherdan Shaqiri has made no secret he harbours a return to Champions Lague football amid supposed interest from Tottenham.