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 Premier League on Sunday - wants to see the transfer wrapped up swiftly.
"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."
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."
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 on Friday it was "possible" Adebayor was about to be sold.
Meanwhile, another wantaway forward Carlos Tevez could be set to make his first appearance of the season for City in this weekend's clash at the Reebok Stadium.
After a fraught summer, during which the Argentina frontman handed in an official transfer request and was unsuccessfully pursued by his former club Corinthians, Tevez returned to training with the Blues last week.
Inter Milan have been linked with the 27-year-old, but it appears no further bids have been forthcoming.
He did not feature in Monday's 4-0 win over Swansea at the Etihad Stadium, but Mancini has already made it clear he would be happy for Tevez to stay and will consider him for the game on Sunday.
"He will probably be available, although I want to wait until tomorrow to make a decision," Mancini said.
"He has worked very well in these two weeks.
"When Carlos plays, he always plays very well and gives 100%.
"I think maybe he is not 100% fit, but his mind is okay."
Mancini must also decide whether or not to hand a first start to Tevez's compatriot, club record ?38million signing Sergio Aguero, who came off the bench against Swansea to score twice and set up another goal in a sensational debut.
Source: Team Talk
Source: Team Talk