The 27-year-old has been assured by Celtic boss Neil Lennon of his role in the team.
Liverpool reportedly made a move for McCourt just before the transfer window closed last month.
“It’s rare something would happen to you on transfer deadline day without you knowing so I wasn’t going anywhere,” McCourt told the Daily Record.
“Of course signing for Celtic was my dream but, at the end of the day, I want to play more football. That has been at the back of my mind a couple of times but I’ve spoken to the boss and I’m very much part of his plans.
“It’s obvious anyone would rather play regularly than be on the fringes of the squad for the duration of their contract and I’m no different.
“I’ve enjoyed my three years at Celtic but, as much as I love the club and being part of the club, I want to play. If I was to leave it would be with a heavy heart but it isn’t going to happen so I’m fully focused on playing for Celtic.”
