The Tykes sacked Flitcroft, who defied the odds to keep them in the Championship last year, at the end of November after a poor run of results left them mired in the bottom three once again.
Mellon, himself a former manager at Fleetwood, has been handed the reins on a part-time basis since and the club appear willing to give him a chance to stake his claim to earn the position permanently.
Flitcroft has since moved on from Oakwell and was this week appointed as the new boss at his former club Bury.
Speaking at his introductory press conference for that job, Flitcroft confirmed he did not expect to be linked up with Mellon again at the JD Stadium.
"Micky, I'm praying he'll get that Barnsley job," he said.
"He's the right man to lead that group, he's the right man to lead their charge.
"He's an incredible human being and I think he will get that job. If he does get that job I lose the opportunity to recruit Micky."
Flitcroft does not harbour any lingering resentment towards the Tykes for their decision to axe him either, admitting it took him just two days to begin plotting his return to the game.
He added: "You have to get over it. I've got a great family that helped me with that.
"It was 48 hours and then start looking for what else is out there and start building a profile.
"I'm not daft, I knew my next programme was probably League Two or League One. I had an offer of coaching at a few clubs but this is an opportunity for me to prove I'm a good manager.
"I've got this opportunity now which I'll grasp and take and I'm going to give it everything."