McCarthy has been on the books of Palace since the summer of 2019 when he joined from Premier League rivals Everton.
The 30-year-old Republic of Ireland international is out of contract at the Eagles at the end of the season.
TEAMtalk has reported that Celtic are ready to offer McCarthy a long-term contract in January to lure him to Celtic Park on a free transfer next summer.
The report has added that the 30-year-old will have to accept a pay-cut, and if he agrees to terms, then the Scottish Premiership giants will try to strike a deal with Palace to secure his services in the January transfer window and not wait until next summer.
However, according to the report, Aston Villa and Burnley in the Premier League are interested in McCarthy as well.
James McCarthy Stats
McCarthy made 16 starts and 17 substitute appearances in the Premier League for Palace last season, while so far this campaign, the central midfielder has made four starts and one substitute appearance in the league.
Celtic or Aston Villa?
Villa are an established club in the Premier League and will be able to pay McCarthy more in wages, especially as he would not cost the Villans anything in transfer fees.
The Villans have a very exciting team this season, with Ross Barkley (on loan from Chelsea), Ollie Watkins, John McGinn and Jack Grealish playing well in midfield.
However, McCarthy is a Celtic fan, as reported by TEAMtalk, and that could sway him towards a move to the Hoops even if he has to accept a drop in wages.
The Republic of Ireland international is only 30 years of age, and he’ll have to decide between securing his future by getting a last big contract or play for a club he supports.
We’re pragmatic, so we expect McCarthy to stay in the Premier League for one more contract at least.