Sky Sports' Kaveh Solhekol relayed the news:
Kaveh Solhekol @SkyKaveh
Raheem Sterling staying at Man City. Will not be going to Arsenal as part of any deal involving Alexis Sanchez moving in opposite direction2017-8-30 08:57:01
Sanchez is in the final year of his deal at the Emirates Stadium and will leave for free next year if he is not sold or signs a new deal before then.
Per BBC Sport's David Ornstein, Arsenal are only prepared to consider offers for Sanchez that include a player as part-exchange:
David Ornstein @bbcsport_david
Arsenal have rebuffed all approaches from Man City for Sanchez. #AFC stance remains not for sale - unless huge money + player offered #MCFC2017-8-29 20:39:31
Bleacher Report's James McNicholas believes that is the right approach from the Gunners:
I also think it makes sense strategically. Might be our best (only?) chance to get a player of that calibrate in next 12 months.2017-8-29 11:41:13
Indeed, a transfer fee alone—even a large one—is perhaps not worth the difficulties Arsenal will face by allowing their biggest star to significantly strengthen City, who already appear to be in a strong position to challenge for the Premier League title.
Sterling isn't yet at Sanchez's level, but he'd nevertheless be a strong acquisition who could mitigate the Chilean's departure, and at 22 he has a considerable youth advantage too.
City can afford to part with him if they're getting Sanchez in return—given they already have the likes of Sergio Aguero, Gabriel Jesus, Leroy Sane and Bernardo Silva—but it seems he will not be moving.
Without him, Arsenal may well hold their resolve even if City make another large cash offer.