McCoist was put on gardening leave at the end of last year with McDowall placed in charge of the team before he handed in his resignation.
However, a new board has since come in after last week’s EGM and have vowed to make sweeping changes at the club and McDowall is hopeful that could mean a return for McCoist.
“It’s a difficult question because I don’t know what the board’s intentions are,” he said.
“If it was Ally, obviously I work with Ally so that would appeal to me.
“The board will have their own ideas and it’s totally up to them.”
“I’ve got three games in a week, so it is pretty full on with the players at the moment. Nothing is scheduled.
“Everyone knows what my situation is. They are quite entitled to speak to whoever they want to speak to regarding the manager’s position.”