Mulgrew, a former Hoops player, insists McGinn would love to play for Celtic.
Speaking on TalkSPORT, Mulgrew said: “Listen, John McGinn would’ve loved to have went to Celtic. I know John McGinn personally, his whole family are Celtic fans, but it just didn’t happen for whatever reason.
“I think it’s definitely going to be in his head (to sign for Celtic). When you’re brought up in Glasgow, the only teams that you see are Celtic and Rangers – and for you, that’s the pinnacle of football.
“I’d picture myself growing up in the streets of Glasgow, picturing myself scoring against Rangers, that was my dream. That was the top of the world of football for me.
“Because that was all I had seen – I know now that there’s bigger games, but to then eventually score against Rangers and feel that, I know John McGinn will be desperate to do that. Whether that happens or not, I just don’t know.”