Everton are reportedly seeking big-name additions in the centre of the park.
Liverpool's Adam Lallana (L) in action with Everton's James McCarthy
The Toffees are said to be looking at big-name trio Axel Witsel, Kevin Strootman and William Carvalho, prompting Potters boss Mark Hughes to ask about McCarthy's availability.
The Republic of Ireland international is yet to return to training at Everton and is therefore unsure how he'll fit into new boss Ronald Koeman's plans.
Republic of Ireland's McCarthy in action at Euro 2016
The Blues handed McCarthy a new five-year contract last summer, following reported interest from Tottenham Hotspur, though he struggled for form in an injury-disrupted campaign.
Stoke, despite paying a club-record fee for Giannelli Imbula in January and also tying Glenn Whelan to a new deal this week, appear intent on adding to their midfield ranks.
McCarthy's Republic of Ireland teammate Glenn Whelan (L) signed a new contract this week
25-year-old McCarthy arrived at Everton from Wigan Athletic in a reported £13 million deal from Wigan Athletic.
McCarthy celebrates with Leighton Baines