McCarthy - who played for Barnsley, his hometown team, and managed Sunderland - is out of work for the first time in six years after leaving Ipswich Town last month.
But a return to Oakwell or the Stadium of Light looks unlikely for the 59-year-old, who the Daily Mail claims 'does not want to work in League One'.
"I want to work in the Championship or the Premier League," McCarthy is quoted as saying. "If I could get a Championship job with a chance of getting in the Premier League, that would be great.
"What gives me inspiration is Roy Hodgson going in at Palace, Warny (Neil Warnock) at Cardiff. Get them organised, hard to beat, know what they are doing. Play good football. Win. I put myself in that bracket."
Both Barnsley and Sunderland disposed of their respective managers, Jose Morais and Chris Coleman, after being relegated from the Championship this past campaign, and appear no closer to appointing successors.
As of Friday morning, the former Mackems boss Simon Grayson is 2/1 favourite to take the Oakwell reins, with Sheffield United's Chris Wilder leading the Sunderland betting at 5/4 - despite reports he is set to commit his future to the Blades (both Sky Bet).