The Scottish Premiership side will take on Old Firm rivals Rangers in the semi-finals of the Scottish Cup at Hampden Park in Glasgow next month.
It promises to be a fiercely competitive match, and one that should have a few goals.
Mulgrew, who can play as a centre-back, left-back or central midfielder, has suggested that the key to winning such a hotly contested encounter is to keep calm.
“I got sent off once in an Old Firm game, at Ibrox,” the 30-year-old told The Scottish Sun. “These games are heated, and it’s important to have experience of them.
“It’s not so much showing you care that matters, because that takes care of itself. It’s keeping calm. The time I got sent off I didn’t do that.
“But I didn’t realise until I looked back at the game how many tackles I’d put in. You need to keep that wee edge, but still be sensible.”
Celtic will consider themselves favourites as they have the strongest squad in Scotland and are also in the Scottish Premiership.
However, Rangers will give the Bhoys a run for their money as they have a much better team than last season.
Ronny Deila’s side got the better of Rangers 2-0 at Hampden Park in Glasgow in the semi-finals of the Scottish League Cup last season.
Celtic could win again this campaign, but the Gers are certainly going to make it tough for them.