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Arsenal’s star forward is set to leave the club this month with his contract still running down ahead of the summer.
Rather than losing him for free, the 29-year-old may well go before the January window shuts.
City have long been favourites to land Sanchez with the Gunners goalscorer keen on the move.
A reunion with Pep Guardiola has been sought, with the two having worked together at Barcelona, and a £20m bid has been put forward.
But United have entered the running after Jose Mourinho tabled a surprise £25m offer.
How Manchester United’s starting XI could look with Alexis Sanchez
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“Liverpool have made contact with the Gunners too”
Henrikh Mkhitaryan could also be offered as part of a deal with Arsenal.
And Chilean journalist Maks Cardenas claims Liverpool have made contact with the Gunners too.
The Reds rivalled Arsenal for Sanchez’s signature back in 2014 when he arrived in England from Barcelona.
And it appears they are also interested in luring him away from the Emirates this month.
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Jurgen Klopp could be turning to Sanchez as an affordable replacement in attack for Philippe Coutinho, with £90m-rated Thomas Lemar proving costly.
Cardenas adds, though, while United, Liverpool and City are in for Sanchez, it is the player’s decision that counts.
Arsenal may have a preference for who he leaves for, but Sanchez wants to play with Guardiola.