The Guardian understand Pep Guardiola's side have submitted a £20m offer for the Chile international, who is out of contract at the end of the season.
Sanchez is said to have been offered a wage-packet of £250,000-a-week over the duration of a four-and-a-half-year contract, which will see him scoop £58.5m until the expiry of the deal in 2023.
In what is now inevitably going to be the final season of his Arsenal career, Sanchez has endured a chequered campaign netting just eight goals in 21 appearances in all competitions.
The 29-year-old's outings continue to be full of the gusto and intensity which has defined his spell in the Premier League but former midfielder Stuart Robson feels the time is right for him to depart.
"The timing is perfect for Sanchez to go," he explained to ESPN. "The Arsenal crowd have fallen out of love with him, [Gabriel] Jesus is injured at Manchester City so he will get his opportunity quicker than he will have done if Jesus and [Sergio] Agueo were both fit.
"It is the perfect time. He can go and win the Premier League, have good go at the Champions League; it is absolutely perfect. He has to go now before it is too late, in case he gets injured."
Despite his departure from The Emirates Stadium appearing to be imminent, Sanchez is expected to start the Carabao Cup semi-final first leg against Chelsea at Stamford Bridge.
Arsene Wenger's side don't play again until the Premier League trip to AFC Bournemouth on Sunday [13 January] and City midfielder Kevin de Bruyne has indicated that Sanchez's move to the Etihad Stadium could be a case of when and not if.
"We will see what happens in this transfer period," he said, according to The Daily Mail. "If a good player comes to us that is better, if he doesn't we do it with the team we have. We are on a good period already. Everybody is doing a good job. When he comes he will add something to the team."