The 28-year-old looked set to be reunited with Guardiola, whom he played under at Barcelona, only for his £60m move to collapse on deadline day after Arsenal failed to secure a replacement.
Sanchez has turned down an offer to extend his deal at the Emirates and the Gunners looked resigned to losing him either in January or for free next summer, with the striker allowed to speak with foreign clubs in the New Year.
While Arsene Wenger has repeatedly insisted neither Sanchez nor Mesut Ozil, who is also out of contract at the end of the season, will be allowed to leave in January, City believe the Gunners' boss can be persuaded to accept a bid in the winter transfer window.
Asked whether the duo would remain in north London, Wenger said last month: "I am not the only one who can decide that. They have a part to play in that as well. If it is my decision, then yes. We have said it many times.
"I rule it out. I don't think every day about that. As long as they are here they give their best for the club. In my head they stay until the end of the season. Unless something unbelievable happens I don't see that changes."
According to the Independent, the Premier League leaders are quietly confident that an agreement with Arsenal can be reached, as long as the north Londoners find a suitable replacement for the Chilean, who has scored five times and made three assists in 14 appearances,
City, however, are aware of the need to table a sizeable offer, potentially in the £50m region, for the forward and are reportedly prepared to do so, despite the fact they could sign the former Barcelona and Udinese player for free at the end of the season.
Guardiola's men have already plundered in 46 goals in just 15 Premier League games so far this season and Sanchez's arrival could see one of Gabriel Jesus, Sergio Aguero and Raheem Sterling demoted to the bench.
The latter will reportedly not open negotiations with City over a new contract until after the upcoming World Cup this summer.
The Mirror reported earlier this week that Sterling, who turns 23 on Friday (8 December), wants to put contract talks on hold to focus on helping City to win the title and on maintaining his form ahead of the World Cup.
Real Madrid are understood to be monitoring the situation after they were linked with the England international two years ago and their interest could be revived, should contract negotiations fail to progress as expected.