With discussions between the two clubs believed to have been going on for some time, it had been expected Nasri might be confirmed as a City player this week.
No such announcement has been made as yet, but Mancini - whose side face Bolton in the Barclays Premier League on Sunday - wants to see the transfer wrapped up swiftly.
City bound? Samir Nasri looks set to leave Arsenal for Manchester City
'I hope we can close it very quickly now, but I don't know the last news about him because my concentration is on the game,' Mancini said.
'But I hope - also because the market finishes in the next 10 days.'
Business as usual: Nasri in training with Marouane Chamakh
Asked why there may have been a delay in proceedings, Mancini said: 'I don't know - this is not my job.
'I don't know why, but it is probably because Nasri is a good player, or because there is some problem.'
Frenchman Nasri's contract at the Emirates is up at the end of the season and he has refused to sign a new deal.
He has not featured for Arsenal so far this season and would be a major boost to Mancini, adding creativityto his side as they look to mount a serious title challenge.
Exciting times: Roberto Mancini is leading Manchester City into a new era
In terms of potential outgoing personnel, one player who seems certain to leave City is Emmanuel Adebayor.
Spurs boss Harry Redknapp this week revealed Spurs were in talks with the Blues about a move for the striker, although Mancini would only say it was 'possible' Adebayor was about to be sold.
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