The former Inter Milan boss guided City to their first trophy success in 35 years by landing the FA Cup last season and has further strengthened his position this term by leading the big spenders to the top of the Barclays Premier League.
But Mancini has just one more year left on his contract after this season and, although he insists his own future is 'not important' right now, his comments suggest he is keen to show his employers his commitment to the cause.
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City have made their best start to a league season since 1897 by winning seven and drawing one of their opening eight games.
The Italian's handling of the ongoing controversy surrounding forward Carlos Tevez has also earned him plaudits, but he says discussions over a new contract have not begun and are not a priority.
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The 46-year-old, who succeeded Mark Hughes in December 2009, said: 'I would like to stay here for many years in the future but it is not important, my contract.
'After this year I have one more year and I don't have a problem with this.
'I haven't talked to the club but at the moment it is not important.'
Mancini is well aware, however, of the vulnerable nature of his profession. City are playing in the Champions League for the first time this season and face a vital game against Villarreal at the Etihad Stadium on Tuesday.
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City have collected just one point from their opening two games and further disappointment in Europe could cast a different light over the club's campaign.
Mancini, speaking at his pre-match press conference, added: 'My feeling here is good.
'I would like to stay here but in football every week it can change.
'If you lose two or three games, that can change all - but we are working well.'
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