The Hoops will learn their European fate when the draw takes place in Switzerland on December 20 and Mulgrew is yearning for a United Kingdom clash in the first knockout phase.
"I would like to face United because it would be a Battle of Britain," he said.
"I have seen those games but never been involved in them so that would be my choice. I'm not going to say I fancy my chances against United.
"But I'm sure we would compete and do everything we could to get some kind of result."