The 29-year-old forward is out of contract at the Emirates Stadium this summer and has been linked with a January move to City.
However, Sky Sports Italia claim Jose Mourinho is plotting to snatch Chile international Sanchez from under their Manchester rival's noses.
United boss Mourinho, who said he was unlikely to buy anyone in January, recently bemoaned his club's inability to invest up to "£700m" in new players, claiming Premier League leaders City have the advantage of unlimited spending power.
Elsewhere, Francis Coquelin has agreed to join La Liga side Valencia on a four-and-a-half-year contract following a decade with Arsenal, the Spanish club announced today.
Coquelin, 26, arrived at Arsenal from French side Laval in 2008 and went on to make 160 first-team appearances.
Meanwhile, Burnley boss Sean Dyche has confirmed the future of Scott Arfield remains in doubt with the midfielder yet to sign a new contract at Turf Moor.
The former Huddersfield Town player has six months left on his current deal and is reportedly attracting the attention of a number of the Clarets' Premier League rivals, including Saturday's opponents Crystal Palace.
Dyche said: "We have had talks with him and he has sat tight on an offer so we will keep an open mind and we will see what comes next.
"Scott knows where it all stands and he knows the club's situation. He's been a very, very good player for us and he continues to be."
And finally, Carlos Carvalhal is determined to hold onto star defender Alfie Mawson, suggesting Swansea City would only consider selling the England Under-21 defender if they received an offer in the region of £50m.
Mawson has been heavily linked with Watford and West Ham United in the January transfer window, while Celtic and Everton are also reportedly interested in the 23-year-old Londoner.
Swansea signed Mawson from Barnsley for £5m in August 2016 and he has two-and-a-half-years left on his contract at the Liberty Stadium.
But Carvalhal insists buying rather than selling is on the agenda of the Premier League's bottom club this month, with the Portuguese saying that chairman Huw Jenkins has given him assurances that Mawson will not be leaving the club.