Roberto Mancini is threatening to end Manchester City's long pursuit of Samir Nasri if the Frenchman becomes ineligible for the Champions League by playing for Arsenal in their play-off second-leg match at Udinese on Wednesday.

City are the early leaders of the Premier League after continuing their winning start with a 3-2 victory at Bolton Wanderers, but Mancini admitted being alarmed by Arsène Wenger's declaration that Nasri could feature for Arsenal and warned it is a "possible" deal-breaker.

The City manager hopes a £25m deal can be concluded "in the next 24 hours, maybe 48 hours" but that account differs vastly from Wenger's, who described it earlier in the day as "a long, long way away". Arsenal's manager made it clear he is willing to pick Nasri, regardless of the possible ramifications for the deal. "I wouldn't worry about that," he said. "What is important to us is to qualify."

Mancini said that would be a "big problem" and asked whether it was a serious enough issue for him to change targets, he nodded and said it was "possible". Nasri would be unable to feature in City's Champions League campaign if he plays at Udinese, even if Arsenal were to lose and not make the group stage.

There was clear frustration from Mancini as he reflected on the inability of the City board to finalise the deal before now. "It's a big problem. For 40 days [I've been saying]: 'I hope it's two days, three days, two days, three days.' I don't know why we didn't close it.

"If he plays in the Champions League [for Arsenal] it is a big problem. I don't know [if we would still sign him]. I'm sure we can close the deal. But it's a problem because we have followed Nasri for 40 days and it's important we take him. Also, for Nasri, I think it will be important [for him] to play in all the Champions League."

Alongside Wolverhampton Wanderers, City are one of only two teams in the Premier League to win their first two league matches, with David Silva, Gareth Barry and Edin Dzeko scoring the goals.

Mancini was entitled to think his team should have won more handsomely on a day when Silva and Dzeko persistently menaced the Bolton defence, but Sergio Agüero was unable to repeat the devastating form of his two-goal debut against Swansea. Agüero eventually made way for Carlos Tevez, who was given a warm reception from City's fans as he played his first match since trying to engineer a move out of the club. The early league leaders have scored seven goals in two games but Mancini was not entirely satisfied, complaining they had been guilty of "stupid" defending.

"It was incredible that the game finished 3-2," he said. "We played very well but it's impossible this game was open until the last few seconds and if we want to have a good championship [title bid], we can't concede goals like this.

"Both were stupid goals because we were dominating the game. We lose one ball – and then it's a goal. If you don't mark [for the second] it is a problem. We had many more chances [than Bolton] but until the last second the match was open and it was possible for the game to finish 3-3. We have to pay more attention."

Mancini went on to speak of his belief that City are still not ready to balance playing in the Champions League with a sustained title challenge and, asked whether he expected Nasri to be the club's last signing of the summer, he replied: "I hope not."

City's directors have already told their manager that the most he can hope for, beyond Nasri, is a possible loan arrangement, but the Italian refuses to change his opinion. "We need some [more] players if we want to complete our team," he said. "I hope he [Nasri] is not the last one."

Tevez, he continued, is almost certain to stay at City. "Carlos has a value. He is an important player, a top player for us, and we haven't received any bids for him for his value."

Still officially the club captain, Tevez came on in the 68th minute but did not take the armband from Vincent Kompany. Mancini, however, said he has still not decided whether to remove the captaincy from the Argentinian. "We have another week [to decide]. At the moment the captain is Vincent. After that, we will see."