Maatsen enjoyed an excellent loan spell with Burnley last season and returned to Stamford Bridge this summer with just 12 months remaining on his contract.
Chelsea have attempted to convince Maatsen to sign a new deal but the 21-year-old Dutchman is yet to agree terms, and his future was complicated late in the transfer window when Chelsea agreed a deal to sell him back to Burnley.
An initial loan was set to be followed by a permanent transfer worth £31.5m next summer, but Maatsen himself rejected the chance to reunite with Vincent Kompany at Turf Moor.
With the transfer window now closed, Chelsea are keen to tie Maatsen down to fresh terms. Manager Mauricio Pochettino is known to be a fan, having handed the left-back four appearances so far this season, while left-back competition Marc Cucurella has been restricted to just one outing in the Carabao Cup so far.
Maatsen's expiring contract has attracted interest from a number of sides across Europe and 90min understands Premier League and Champions League winners City are among the suitors of the Dutchman.
Finding a natural left-back has been among City's top priorities for months and a cut-price move for Maatsen would appeal to Pep Guardiola's side, although the ball remains in Chelsea's court after the transfer window closed.
Talks between Maatsen and Chelsea will continue over the coming weeks with regards to an extension and sources close to the situation believe Chelsea are hopeful an agreement will be reached soon.
Back in pre-season, when Maatsen emerged as a first-team player under Pochettino, the left-back made it clear he wanted to remain at Stamford Bridge this season.
"I try to do my best," he explained during the summer. "It’s all I can do. Of course I want to stay. If I prove that every day in training and work hard in the matches, they’ll decide. Hopefully I can stay here."
