The 25-year old is likely to be deployed at left-back by manager Neil Lennon with reigning Scottish Premier League Player of the Year Izaguirre likely to be sidelined for up to six months following the injury sustained at Aberdeen last weekend.
Mulgrew is well aware that the absence of the Honduran could make life tough for the Hoops but says he is looking forward to taking his opportunity and hopefully cementing his place in the Hoops' first team.
"Emilio's injury is very disappointing for everybody, he will be a big loss to the team and everybody is gutted for him," he said.
"I don't know if it's my preferred position but I can play there. I've played there a lot and I'm comfortable there.
"Wherever I play, I just try to do my best and if I play well, I enjoy it. I don't have a preferred position.
"You can't think like that, you've got to think about your own game," he said about filling Izaguirre's big boots.
"You can't compare yourself to other people. You've got to come in and do the job you know you can do and get on with it.
"I've got to believe in myself and if I'm chosen to play there I have to do my best and I'm confident I can do a job there."