The former Republic of Ireland manager has rejected an approach from his hometown club, with his last managerial role coming with Cardiff City, a job which he departed in October 2021.
Barnsley suffered relegation from the Championship just 12 months removed from competing in the play-offs with Valerien Ismael.
A disappointing campaign saw both Markus Schopp and Poya Asbaghi depart the club, with neither able to follow on from the good work Ismael had done previously.
The club are hoping to appoint the next head coach by June 13, or ideally before pre-season gets underway.
Neil Warnock has also been contacted over the vacant position.
Both managers would represent a change in direction for the club, but the board was overhauled following this campaign which now seems to have opened the door to different thinking by the decision makers.
Warnock had announced his retirement earlier this year, but it now appears that he would be open to returning to the club that he played for between 1976 and 1978.
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McCarthy also played for the Tykes during his career, but that has not swayed him to take over the third tier side.
Warnock holds the record for most promotions earned in English football history, having brought eight teams up a division during his career.
There are also five or six other names on the shortlist to take over the team, including Manchester United coach Eric Ramsay.
McCarthy initially started well during his last managerial role at Cardiff, before ultimately running into a poor run of form that led to his dismissal.
His previous stint with Ireland before that was also extremely poor, with a turgid style of football failing to get any decent results.
This wouldn’t have been a very inspiring appointment, even if he likely could have led the team to promotion.
A decision will need to be made soon on the next manager, with pre-season coming earlier this year due to the calendar disruption caused by the winter World Cup.