Despite his emotional connection to the club, having grown up as a Celtic fan, he still quit to return to the Premier League.
He has previously made it clear that he does not regret his departure from Celtic, insisting that Leicester was a step up for his career.
“I’ve always said it was such a tough decision for me to leave Celtic. What I couldn’t do was let my heart rule my head. I felt like I needed a next challenge,” he told Sky Sports earlier this year.
But that may leave Leicester fearful that history could repeat itself if United do indeed come calling for their manager.