The alleged offer comes just days after Sterling, who has signed for a record £44m plus add-ons from Liverpool in 2015, scored a dramatic late winner for City against Bournemouth on Saturday. He had previously scored a well taken equaliser to rescue a point against Everton.
At face value, it would seem that City boss Pep Guardiola sees the English winger as a necessary sacrifice if he is to reunite with Sanchez and turn his squad into title contenders.
But it is Sterling's fine start to the season that makes the story hard to digest. It would also represent the ultimate in short-termism from a club who have made a huge effort in recent years to come across as wholesome, with a 22-year-old with untapped potential making way for an established player who will turn 29 in less than four months if a deal genuinely materialises.
One thing that does appear to lend some credence to the story is a report from Chilean outlet T13, which suggests that Sanchez has requested permission for some time off from his duties with the national team on Wednesday afternoon for 'personal business'.
Whether the player has made the request to coach Juan Antonio Pizzi proactively in the hope that he might need the time to complete a transfer, or if he actually needs the time because something is already in the pipeline is not yet clear.
Sanchez has still not signed a new contract at Arsenal and the club run the serious risk of losing the ex-Barcelona player for free next summer unless they are willing to sell him now.
Manager Arsene Wenger has remained steadfast that Sanchez will not be sold, but the danger that the club's most valuable asset walks for nothing in less than a year's time is very real.