Victory at Parkhead could see the Hoops clinch the Clydesdale Bank Premier League title, if nearest rivals Motherwell lose to St Mirren.
And, with a William Hill Scottish Cup semi-final against Dundee United looming, Mulgrew believes those given the nod against Hibs could also be playing for their place at Hampden.
The defender 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."
Hibs are one of four teams who will be battling to claim the final top-six spot this weekend.
Mulgrew added: "It will be a very hard game. Like any team that comes to Celtic Park, they are very motivated.
"It's one of the big games of the season for them and we will need to match that."
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