McCarthy is the bookies' favourite to return to his hometown club and replace Paul Heckingbottom at Oakwell.
However, HITC Sport understands McCarthy will reject any overtures from Barnsley and plans to stay at Ipswich.
The news will come as a blow to the Tykes as they continue their search for a new manager with Lincoln boss Danny Cowley set to stay at Sincil Bank, while Simon Grayson is poised to become the new Bradford City boss.
McCarthy, who made 272 appearances for Barnsley during his playing career, has been at Ipswich for five years and has done an impressive job on a shoestring budget at Portman Road.
The former Republic of Ireland and Wolves manager has continually steered Ipswich away from relegation trouble and made the play-offs in 2015 while also agonisingly missing out on the play-offs again in 2016.
The 58-year-old is out of contract at Ipswich at the end of the season and, as yet, there have been no indications of a new deal to keep him in Suffolk.