McMahon said: "He's very shrewd and he should be part of it, in my opinion anyway. He knows the culture of the club, he knows what's needed and I think he would be instrumental in getting the right manager.
"If they're going to ask him, he'll probably say 'give it to me', because I think he'd love to do it again. And I think if they don't ask him, he'd love to be part of the process anyway.
"What a fantastic footballer in the first place and argubaly even a better manager. To win the double in your first season put him up there with the best. He was a great man-manager, he knew his players, he didn't do much coaching, but he could pick the players. He certainly knew what a player was."
McMahon, speaking to Rob McCaffrey on Soccer Extra, also insisted that former Reds boss Houllier was wrong to criticise former players such as himself who had aired their views on the modern Liverpool set-up.
He added: "It's not a case of the ex-players wanting Liverpool to do bad, they don't. They want Liverpool to be successful and they're only venting their feelings - for the right reasons, not the wrong reasons.
"They didn't want Gerard Houllier out. All they wanted was to win games and be challenging for the major honours and that hasn't happened and it had to come to this. It really did.
"For him to put ex-players under pressure was wrong, I thought. They're entitled to their opinion and some of them are earning a living, so they can say what thety like within reason because it's constructive criticism and you've got to eb big enough to take that.
"It's not just the signings, it's the way they set their stall out. I think they've got a bit more adventurous over past 12 months or so, but the way they set their stall out to play on the counter-attack, Liverpool fans haven't seen that before.
"They're a patient bunch, they give you time to win games and certainly they're educated as we all know. But it was frustrating to watch."