Mulgrew is one of four Parkhead players in the Scotland squad for the match against Wales, with Adam Matthews and Joe Ledley both slated to start for Chris Coleman's side.
It adds a new meaning to the phrase Celtic connections and Mulgrew is hoping to get one over his club team-mates to bolster Scotland's chances of qualifying for Brazil 2014.
He said: "It will be strange lining up against Joe and Adam if we get picked – guys I play with every week.
"I have had a bit of banter with them about the game but probably won't speak to them again until we get back now. We are looking forward to the game and, hopefully, we can win it.
"It is a massive game and the manager has made us aware of that in training. We will all be striving to get three points. Our main focus is to win the game tomorrow, which would be a massive boost for us.
"We are not thinking too far ahead or what other teams are doing or not doing. It's up to us and it is still in our hands so we are looking to win this game."
Mulgrew has played in a number of positions for Celtic – left-back, central defence and in midfield – and hopes his versatility will stand him in good stead with Scotland.
The return of Danny Fox from injury might limit Mulgrew's chances of starting at full-back, but he hopes Craig Levein will keep him in mind for whatever role.
He added: "I don't know where I will be playing. It is just wherever the manager sees me playing, I have not spoken too much to him about it. At the back is probably where I have more of a chance.
"It is an advantage I can play a few positions and I am sure the manager is well aware of that. Whatever he has in mind for me, I am happy to do a job."
Gareth Bale will likely be the main dangerman for the Welsh but Mulgrew warned they were more than a one-man team.
"Bale is quality and world-class player – he will be one we need to watch. His performance against Inter Milan a while ago for Spurs just showed how he is a top player.
"He is very fast and causes teams a lot of problems so hopefully we can match him. But Wales have got a few top-class players and I am sure we will be fully prepared for them."