But United's interest, if true, will probably leave Arsenal in no mood to reduce their asking price, even though Sanchez can walk away for free in the summer.
And while the United boss was not drawn on reports of their bid for the player, he admitted the club have a duty to be in the market for that sort of calibre of footballer when they become available. There is no doubt about that, the club are interested.
"I don't know if it's ethical or correct to be speaking about players of other clubs", said Mourinho.
"My approach to players is that every player has a price, it doesn't matter who he is, doesn't matter his level or prestige, I think every player has a price."
There has been speculation over the futures of both players, with Real Madrid said to be interested in them.
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However there is no way Alexis Sanchez will agree to this. We do not believe in signing a player just to do something.
"But we want to keep Jack [Wilshere] and if we have an opportunity maybe to keep Ozil, the rebuild will be less deep than if all the three left".
Sanchez has familiarity with City, as he previously played under manager Pep Guardiola at Barcelona.
City and Sanchez's representatives had agreed to personal terms of about £250,000 a week before the move collapsed in August, and sources said a similar pay deal would be in place should he move to the Etihad this month.
"Of course I want a quick resolution", he told reporters at Arsenal's north London training base. The striker believes lack of opportunities for Liverpool could mean he doesn't make it into Gareth Southgate's England World Cup squad this summer. Certainly not, but there's always a way to find a different balance.