The Guardian says City's confidence is based on the knowledge that Sanchez, 28, is keen to play under Pep Guardiola again.
However, Arsenal are reluctant to sell their star forward to a domestic rival and would prefer to let him join overseas clubs such as Bayern Munich or Paris Saint-Germain.
Sanchez only has a year left on his Gunners contract and has so far refused to sign an extension, with reports claiming that he has been offered around £250,000 a week by the north London club to extend his stay at the Emirates Stadium.
The Chile international played one season under Guardiola at Barcelona, with the pair winning one Copa del Rey together at Camp Nou.
The forward, who helped Chile beat Portugal in the Confederations Cup semi-final on 28 June, admitted in May that he was "frustrated" with Arsenal's season and that he would make a decision on his future in the summer.
His national team boss Juan Antonio Pizzi said he had not been unsettled by speculation surrounding his future at Arsenal.
"We think he's very happy. He's giving his best like everyone else," Pizzi was quoted as saying by Sky Sports.
"Everybody would like to be at the best clubs in the world, he is already at one, and everyone wants to have him in the squad. He's very focused and he knows exactly what he has to do.
"We will see what happens in the future. Right now he feels very comfortable and he's committed to the national team."
Meanwhile, Bayern Munich midfielder Arturo Vidal has urged his compatriot to join him at the Allianz Arena.
"We'll see if Alexis is coming. I do not know yet," Vidal told Bild earlier this week. "I know him very well. He is a spectacular player. And with him, we would surely improve.
"We already have a lot of top-level players. We are the best club in the world."