Neil Lennon's team could retain the title this weekend with a victory over Hibernian, should Motherwell slip up against St Mirren.
Regardless of Saturday's results, Celtic require six points at most to be crowned Scottish champions for the 44th time.
And, with a Scottish Cup semi-final against Dundee United on the horizon, Mulgrew believes those given the nod against Hibs could also be playing for their place at Hampden.
Mulgrew said: "At a club like Celtic, there is always pressure and everybody is fighting to get into the team every week, especially when there's a semi-final coming up.
"I'm sure everybody will want to be involved with that game.
"Our focus will be on trying to win on Saturday. It's been a successful campaign for us so far.
"We've had a good run in the Champions League and we're clear at the top of the SPL by quite a few points.
"There is still a lot to be done before we win the league. We'll just need to wait and see what happens on Saturday."