The champions have asked about Sanchez's demands through intermediaries and would be willing to capitalise on any breakdown, although there is a belief United are now too far ahead despite "complicated" negotiations with Arsenal.
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".
Jose Mourinho says Manchester United are prepared to do business in the January transfer window should a "fantastic opportunity" arise as speculation grows that Alexis Sanchez is on his way to Old Trafford.
Sanchez, who now wears the no.7 shirt for Arsenal, is also a target for Manchester City who came close to signing him on the final day of the last transfer window.
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The Arsenal attacker has been linked with both Manchester clubs in recent days but it seems that Liverpool FC could also now be in the hunt for his signature this month.
A bidding war could well ensue meaning Sanchez's eventual fee may not end up being a bargain.
As a result, Sanchez was left with no choice but to stay put in North London, though it has still always been widely predicted that the South American will depart the Emirates, either this month for a nominal fee or for free in the summer upon the expiration of his contract.
"If players like Sanchez go we have of course to respond".
"I still think that Manchester City will wake up and offer the extra money and they will get him". "Today I was completely separate from all of that - I was just focused on my match and not anxious about anything else".