Sanchez, 29, looks to have played his last game for Arsenal, with manager Arsene Wenger saying on Sunday that his move could be confirmed "in the next 48 hours".
A layer of uncertainty as to whether he would opt for the blue or red half of Manchester appeared to end on Monday when, with United en route to a 3-0 home win over Stoke, City let it be known they were no longer interested in signing the forward, although there were reports that Chelsea might enter the bidding.
"No news on Alexis Sanchez, he is an Arsenal player," he told the BBC. "If he stays it's great for Arsenal, if he comes to us, great for us, if he goes to another club, great for them."
The United manager, in a subsequent interview with Sky Sports, was coy when asked if United were now in pole position to sign Sanchez.
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"I've no idea. Today I was completely separate from all of that -- I was just focused on my match and not worried about anything else.
Pep Guardiola's City, whose move for the player collapsed at the end of the summer transfer window, are understood to be reluctant to pay a reported fee in the region of 35 million ($48 million, 39 million euros) for a player who is out of contract at the end of the season.
If the transfer goes ahead it would be the third blockbuster move of the January window involving Premier League clubs following Philippe Coutinho's big-money move from Liverpool to Barcelona and Virgil van Dijk's arrival at Anfield from Southampton.
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And there was speculation on Monday that Mourinho was prepared to let United midfielder Henrikh Mkhitaryan move south to Arsenal in order to help get the deal done.
It certainly looked as if the Armenian was on his way out of Old Trafford after he failed to even make the bench against Stoke.
"He is our player so I can speak about him," said Mourinho. "He has a lot to offer us.
"Is he going to be involved in leaving us? It is possible," the Portuguese added. "The market is open."
City boast a dazzling array of attacking talent with the likes of Kevin De Bruyne, Leroy Sane, David Silva, Raheem Sterling, Gabriel Jesus and Sergio Aguero vying for places.
United also have an impressive selection of forwards but Sanchez could expect more playing time alongside Romelu Lukaku at Old Trafford, with doubts growing over the future of Zlatan Ibrahimovic following his recent return from a long-term injury.
Sanchez joined Arsenal from Barcelona in 2014 and in a stellar 2016/17 campaign scored 30 goals and made 17 assists, though his form has since dipped.
Wenger left Sanchez out of his squad to face Bournemouth on Sunday, where they slipped to a damaging 2-1 defeat, leaving them eight points off the top four.