Aston Villa are also claimed to be interested in securing the services of the 29-year-old former Wigan Athletic and Everton central midfielder.
Leeds, Newcastle, West Ham and Villa have all spoken to Palace in regard to signing the player they paid £8 million for to recruit from Everton in the summer of 2019, according to the report.
West Ham manager David Moyes and Newcastle United boss Steve Brice have been tracking the Republic of Ireland international for a long time and are known fans, according to the report.
The experienced midfielder also played once in the FA Cup and once in the EFL Cup, according to WhoScored.
Crystal Palace stay
McCarthy did well in his first season at Palace, having recovered from the injury problems that had affected him over the years.
While a move to Leeds, Newcastle, West Ham or Villa would be appealing, perhaps it would be best for the former Everton man to stay at Selhurst Park.