The Red Devils are understood to have lodged a £25million offer to sign Sanchez this January, with Manchester City now preparing to withdraw their interest in the 29-year-old Gunners forward.
Initial reports suggested that United would be willing to let Henrikh Mkhitaryan join Arsenal in a swap deal for Sanchez, but it appears Arsene Wenger has his eye on another player.
The Daily Star claims the north London club are demanding Anthony Martial in any potential deal for the Chile international.
However, United are unlikely to let Martial complete a move to the Emirates as the Frenchman is central to Jose Mourinho going forward.
Asked whether United had submitted an offer for Sanchez, Mourinho said: ‘I don’t know if it’s ethical or correct.
‘The word we can find to be speaking about players of other clubs. If somebody speaks of one of my players to tell we are interested or we are not interested, I wouldn’t be very, very happy.
‘Sanchez is an Arsenal player, I don’t know but probably this weekend he is going to defend Arsenal colours so I don’t think it’s correct to say things about Alexis Sanchez.
‘At the general level what I can say is myself and the Manchester United board, the owners, we don’t believe a lot in the January market, we don’t believe in signing a player just to sign a player, just to do something, we don’t believe in that.
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‘What we believe really is there are some players in football world if you have the chance to sign them in January, in March or in July, you have to try and that’s it.
‘But in relation to Alexis Sanchez I don’t say a word, the only word I can say is he is a phenomenal player, apart from that an Arsenal player and I feel I shouldn’t say much more than this.’