However the England international has made no secret he would prefer a role in the centre of midfield.
Milner is Mancini's sixth summer signing after his protracted move from Aston Villa was sealed last week.
Mr Versatility: James Milner can play any number of positions and will happily do so for his new manager, but he would prefer a central midfield role
He said: 'Wherever the manager wants me to play, I'll do it to the best of my ability.
'But I enjoy playing in the middle - that's probably my best position and where I've shown by best form over the past 18 months. I've been most creative and scored goals from there and I've enjoyed it immensely.
'I think that's where the boss has signed me to play, but if he asks me to play anywhere else I'll do what is best for the team.
'As long as we're winning football matches, that's all that counts.'
Milner is up for the challenge at City, who have splashed out in the hope of reaching the Champions League.
'You need competition at any successful club, because if players are comfortable, whether they play well or not then performances are going to slip,' he added on www.mcfc.co.uk.
Man in the middle: Milner hopes his form for Aston Villa last season will edge him ahead of teammates such as Patrick Vieira, left, and Nigel de Jong
'You need players pushing each other every day to step out on that pitch, and if you know you are going to be replaced if you don't perform, then that's healthy for the team.'
While City have rebuilt their squad at vast expense, Liverpool have made only one high-profile signing in England midfielder Joe Cole.
However more significantly for Mancini, new manager Roy Hodgson has kept hold of his best players.
Steven Gerrard has said he is happy to carry on and help Liverpool try and improve on a disappointing seventh place in the Barclays Premier League last season.
Spain striker Fernando Torres, with a World Cup-winner's medal in his pocket, is also up for the fight.
Torres is getting back to full fitness after injuring his thigh in the World Cup final and was on the bench in the draw against Arsenal last weekend.
Despite needing two knee operations during the season he still managed to finish with 22 goals in 32 games in all competitions for his club.
Argentina enforcer Javier Mascherano remains on board even though he has been linked to a move away from Anfield.
Mancini said: 'Liverpool are a strong team. They did not sell any players from last season.
'We want to win but I have a lot of respect for them and a lot of respect for Roy Hodgson. It should be a good match.'
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