That's according to the Telegraph, who say the Gunners will 'explore' a move for the England star as he enters the final year of his Man City contract.
Mikel Arteta, who signed a new deal at the Emirates last week, worked closely with Sterling during his three years as a coach at City alongside Pep Guardiola.
And, if Sterling is available to buy at the end of the season, the Gunners boss is said to be keen on reuniting with the forward and making him a key part of his side's attack.
The Jamaican-born winger has previously said that he would be 'open' to a move elsewhere,
Speaking at the FT Business of Sport US Summit in October 2021, Sterling said: "If there was the opportunity to go somewhere else, I would be open to it at this moment in time."
Arsenal look in a prime position to finish in the top four this season and qualify for the Champions League, which could mean they are capable of attracting players of Sterling's calibre.
The north Londoners will be keen to bolster their attack this summer, as they look to replace Pierre-Emerick Aubameyang and out-of-contract Alexandre Lacazette.
Eddie Nketiah, Bukayo Saka, and Gabriel Martinelli have starred for Arteta's side in recent weeks, helping them to their fourth win in a row against Leeds on Sunday.
And Sterling would add extra firepower to their frontline, having scored 77 goals for Manchester City in the Premier League over the last five seasons.
The Three Lions man, who has now made 74 caps for his country, would add to an already English-heavy squad that Arteta is assembling.
Whilst he is already one of the first names on Gareth Southgate's teamsheet, more first-team football ahead of the World Cup later this year would help him nail down his spot in the starting XI.