The England international, whose contract expires in 2023, worked under Gunners boss Mikel Arteta at City previously and is expected to be a primary target as they look to bolster their squad.
The 27-year-old has been a regular under Pep Guardiola, featuring 45 times, notching 16 goals and picking up a further seven assists in all competitions so far this campaign, including two against Newcastle United in their 5-0 win on Sunday.
The Telegraph says despite still being a key part of City's success, his future remains uncertain with just one year left, but the forward has put talks over his future to one side to concentrate on the Premier League title defence and adding a fourth winners' medal to his collection.
Arsenal, however, are planning to bolster their squad with the potential of being back in the Champions League next season.
Arteta, who recently signed a new contract, will be backed in the transfer market and is looking for firepower to replace Pierre-Emerick Aubameyang and out-of-contract Alexandre Lacazette with Sterling top of the list.
The Spaniard worked closely with Sterling during his three years at the Etihad as a member of Guardiola's backroom staff, before going his own way and becoming the manager of Arsenal.
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