The Independent says Sanchez, 28, would accept an offer lower than the £300,000 ($391,000) a week Arsenal are willing to pay him to link up with Pep Guardiola at the Etihad Stadium.
The Chile international is reported to have made up his mind to reunite with Guardiola, after having worked with the Spaniard at Barcelona.
Citing sources close to Sanchez, the Independent reported that the 28-year-old is unlikely to sign a new deal with the Gunners as he wants to compete in the Champions League and challenge for major honours.
The former Udinese forward said earlier this month that he had made his wishes to play in the Champions League clear to Arsenal. The Gunners will compete in the Europa League in the 2017/18 season after their fifth-place finish in the Premier League last campaign.
"The truth is that the decision [on my future] doesn't depend on me," the 28-year-old was quoted as saying by the Guardian.
"I have made my decision, but now we wait for a response from Arsenal. It depends on them, I have to wait to know what they want.
"My idea is to play and win the Champions League, it is a dream I have had since I was little."
Gunners boss Arsene Wenger insisted at a press conference in Beijing on 24 July that Sanchez would not be going anywhere this summer.
"My mind has been made up for a while now. I think I've made it clear a few times; that this is my stance," the Frenchman was reported as saying by Sky Sports.
"We are in a strong financial position. Sanchez has got one year to go on his contract and we have no need to make money.
"He will be part of the team next year and after that I can understand [if he wants to leave]."