Mancini went public with his interest in Nasri during the close-season after City made a £25 million ($36m) offer for the France midfielder, who is believed to be keen to move to Eastlands in a deal that would more than double his wages.
But City have so far been unable to conclude a deal with Arsenal and Gunners boss Arsene Wenger decided to play Nasri in Saturday's match against Liverpool.
That surprise move sparked reports that Nasri's agents were endangering the deal by demanding a ?£3 million fee for facilitating the transfer.
However, Mancini is confident Nasri will become a City player eventually and he said: "I hope we can have the player in the next days.
"I don't know what's the problem. I hope this week we can have Nasri, but don't know when. We have 10 days to the end (of the transfer window)."
Mancini was speaking after his side won 3-2 at Bolton Wanderers to secure their second successive victory in the Premier League.
The Italian was happy with City's attacking performance, which featured goals from David Silva, Gareth Barry and Edin Dzeko, but warned they will need to tighten up in defence if they are to challenge for the title.
"We played very well," he said. "But we suffered until the last second because Bolton are a good team who will always try to score.
"We can't concede two goals like today. We need to pay more attention. If we want a good championship we should pay more attention in these sorts of situations.
"I want us to score 15 goals more than last year but we can't concede more goals than last year."
Meanwhile, Bolton manager Owen Coyle is convinced his side can recover quickly from the loss after giving a good account of themselves against the Premier League's big spenders.
"We gifted them a couple of goals and that leaves a bad taste in the mouth," Coyle said.
"But we'll pick ourselves up. Our strength is always as a group and we showed that when we picked ourselves up from two down and then 3-1 down.
"We've shown that whoever we play it's certainly going to be a tough fixture for them."
Source: AFP
Source: AFP