With only months remaining on his contract and the ability to negotiate with new clubs for a summer move on the free, the Blue side of Manchester is standing pat on their reported price.
The United boss spoke further about 'Chicharito' in July when his move to West Ham was being processed, expressing regret that he had been sold.
Press Association Sport contacted both United and Arsenal with the Manchester club saying they were not aware of any bid for Sanchez while the Gunners declined to comment.
It was suggested fierce competition between City and United over the services of the former Barcelona forward could be to Arsenal's advantage, but the manager gave little indication an auction is underway behind the scenes.
"I have a good relationship with Theo and I don't want him to be frustrated or lose an opportunity to go to the World Cup".
"But there is always a way, to find a different balance".
Of all the candidates, we'd wager that Mahrez ending up at the Emirates come February is the most likely, perhaps to the tune of £30million-odd.
Will he go to Premier League leaders City or have United found a way to persuade him to choose Old Trafford?
With Man City, off the table, however, Man United would have a free run at trying to convince Sanchez to join them this month. You conclude [that Manchester United are also interested] - but I don't want to give you the wrong information.
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"If you want to achieve something good, win titles, you have to not just win but win at these kind of stages".
You can see the logic behind the deal for the two clubs. The 21-year-old Gremio midfielder is expected to make the Brazil World Cup squad and reportedly has a £45m buyout clause.
"I don't rule it out". "If I was my players I wouldn't want my manager talking about other things".
"So what is the player's calculation?"
City were of course in a similar situation with Dani Alves last summer.
What type of player is he? Lingard and Martial have as many goals as the South American but Sanchez's overall Premier League record for Arsenal of contributing a goal or an assist every 119 minutes is difficult to ignore.
The Telegraph suggests Conte has 'recommended' Sanchez once again as the Italian grows increasingly frustrated with the Blues' lack of action in the transfer market.
But yesterday it emerged that United had made a late attempt to sign him, offering Henrikh Mkhitaryan as part of the deal as a sweetener to Arsenal.