In the final days of the summer transfer window, reports suggested that City had made a desperate attempt to bring Alexis Sanchez to the club by offering Sterling in a cash-plus-player deal.
Pep Guardiola later claimed that it was Arsenal who had submitted the proposal, one which was emphatically rejected by the two-time Premier League champions, and insisted the England international would not leave the Etihad.
However, according to the Daily Mail, Arsenal are prepared to test the Premier League leaders' resolve again in the January transfer window, as they expect City to make a move for Sanchez.
The former Liverpool winger has hit the ground running this season, scoring 10 goals in 15 appearances in all competitions, which means he has already equalled his tally in the last campaign.
Given Sterling's sparkling form, it remains to be seen whether Guardiola would be prepared to allow the England international to leave, even if that meant landing Sanchez.
"Raz [Raheem] is staying here," Guardiola said at the end of September. "The club trust him, that is why we have invested a lot of money in him, so the players we have are going to stay. If they want to leave they are going to leave, but he wants to stay. If players want to leave they have to ask the chairman, but there is no chance of that. He is going nowhere."
The Premier League leaders could table a new offer for the Chile international in January after their bid to land the Arsenal forward collapsed on deadline day, when the Gunners failed to secure a replacement.
However, while City's offer in August was believed to be in the region of £60m (€66.8m), the two-time Premier League winners are likely to bid considerably less for the former Barcelona forward, who will be able to leave the Emirates for free at the end of the season.
Meanwhile, the Gunners are reportedly ready to bow out of the race Monaco star Thomas Lemar, which would leave Liverpool and Barcelona to fight it out for the France international.
The Gunners were ready to shatter their transfer record on deadline day last summer, making a £90m bid for Lemar but failed to get the deal over the line in time. Liverpool also emerged as a serious contender to sign the 22-year-old late on, making two bids in the final week of the window, but it was Arsenal who came closest to striking a deal, as later revealed by Monaco vice president Vadim Vasilyev.
However, according to The Mirror, Arsene Wenger's side are now fearful a deal will be "impossible" given growing interest from Champions League clubs who will be ready to offer the player a better deal.