Veteran defender Mulgrew and main striker McNulty were forced off by muscle injuries in Thursday's Premier Sports Cup defeat by Hibernian.
Manager Tam Courts is hopeful neither issue will prove to be long term but confirmed both players would miss out against Ange Postecoglou's side.
He said: "Charlie and Sparky are both influential players for us, so to lose both of them against Hibs was really frustrating."
Courts and Postecoglou are both still in their early months as managers of United and Celtic respectively as they prepare to lock horns for the first time.
"Celtic are probably similar to us in that they're a team on a journey," Courts said.
"They've had a strong start to the season, they've recruited a number of players and, like us, they'll have some steps forward on their journey and at times they might have a few steps backwards or sideways.
"But definitely a team on a journey right now - and doing quite well. It's really exciting to be coming up against them.
"Personally, everything that I'm experiencing just now is a first - my first time going to Celtic Park, my first time facing Celtic, first time facing their manager, so everything's exciting."