Samir Nasri has returned to training with Arsenal with the French midfielder currently content to play out the final year of his contract if the club do not receive a sizeable enough offer to tempt Arsène Wenger into selling him.

Arsenal have already dismissed Manchester United's opening offer, thought to be just under £20m, with the London club rejecting it out of hand and not even deeming it worthy of a formal reply. That stance has reinforced the feeling within Old Trafford that Wenger is rigidly sticking to his promise not to entertain the idea of doing business with any of Arsenal's Premier League rivals, and particularly United.

The feeling at the Emirates is that any serious bid would have to start at £25m and, even then, United are not entirely convinced that Wenger would be willing to sell to them if Arsenal can generate offers elsewhere. Senior figures at Old Trafford know, for example, how intensely they would fight any bid from another top-four club for one of their top players, citing the lengths they went to in 2007 to prevent Gabriel Heinze joining Liverpool.

They also have extreme doubts that Wenger would be overruled from within the club and there is a realistic view at Old Trafford about the complications of negotiating with a major rival and the hurdles that have to be crossed if Nasri is to become their fourth major signing of the summer, taking their net spending beyond £70m.

Nonetheless, they are prepared to take their interest as far as they can and are encouraged by the sense that Nasri wants to move to Old Trafford, both because of the finances on offer and the frustrations that he feels about Arsenal's failure to win a trophy since he joined the club from Marseille in 2008.

Arsenal have come up with a new contract worth £90,000 a week, which would make him the club's equal highest earner alongside Cesc Fábregas, but the 24-year-old is conscious that while this is the club's best offer – Wenger is not prepared to break his rigid pay structure – United could offer him a contract of more than £100,000 a week.

Nasri completed morning and afternoon sessions on his first day back at the club's training ground but it is not thought he spoke about the situation at length with Wenger and it remains unclear when that time will come.

If the impasse continues, the danger for Arsenal is that he could run down his contract and leave as a free agent next summer, just as Mathieu Flamini did in 2008 when he left to join Milan after turning down a contract extension.

Manchester City are among the other clubs considering putting in a counter offer, while Chelsea and Internazionale are also monitoring the situation.

Nasri, meanwhile, will be on Arsenal's pre-season tour to Asia when the squad fly out on Sunday. With Fábregas keen to finally make the move back from Arsenal to Barcelona, Wenger is conscious that if he were to lose his captain and Nasri, following this week's transfer of Gaël Clichy to City, this would send a negative signal to his rivals.

Nasri has already stated that he would consider a move to United, saying last month: "I don't know if I will sign a new contract. Anyway, the discussions are ongoing."

Arsenal's two-match tour to Malaysia and China features games against a Malaysia XI and Hangzhou Greentown before they return home, ahead of travelling to FC Cologne for a friendly on 23 July.

Wenger will hope he has resolved Nasri's future by then, though the situation has the potential to become one of the summer's long running sagas.