The teams meet at the Aviva Stadium with the Irish two points behind third-placed Scotland, who won 1-0 – courtesy of a Shaun Maloney goal – when they met at Celtic Park last November.
Republic of Ireland manager Martin O’Neill admitted earlier this week this was a game his team cannot afford to lose but Mulgrew said Scotland are not putting similar pressure upon themselves.
“If we can win the game it will be a step in the right direction but we are only halfway there. We are not getting carried away,” he said.
“It is not a must-win game or anything like that for Ireland or us. We are just looking to pick up the three points if we can. The last game was very physical and we expect the same again.
“They have a lot of very physical players and we have players who can do that as well so it will be a typical British game.
“We know the threats they possess and they goalscorers in the team. They have a physical presence which can cause problems so we need to be ready for that.
“We are not thinking there is a lack of goals there or anything like that and we are prepared for the best Ireland can produce.”
Italian referee Nicola Rizzoli, who officiated at last year’s World Cup final between Germany and Argentina and Liverpool’s Champions League game with Real Madrid last October, will be in charge on Saturday evening.
Republic of Ireland boss O’Neill was in a relaxed mood as he spoke to reporters ahead of Saturday’s game at the Aviva Stadium but refused to divulge any details regarding his team selction.
O’Neill said: “I have an idea about the side but there is plenty of time between now and Saturday.”
You can watch Scotland take on the Republic of Ireland from 4pm on Saturday on Sky Sports 1 HD.