The former Manchester City man has been deemed surplus to requirements at Stamford Bridge alongside the likes of Ben Chilwell and Trevoh Chalobah.
As a result, Sterling has not featured in any of Chelsea's four matchday squads this season, leaving him searching for a new club before the transfer deadline.
Man United had emerged as a potential contender as reports suggest Sterling could move in a swap deal involving Jadon Sancho.
Arsenal are also in contention to sign Sterling, with the player said to have a strong relationship with Arsenal manager Mikel Arteta from their time working together at Man City.
Arsenal pursuing Sterling move
Earlier in the day, it was reported that Arsenal were unlikely to strengthen their attacking options before the 11pm (BST) deadline.
However, according to The Athletic, the Gunners are now actively working on a deal to sign Sterling before the transfer window slams shut.
The update claims that Arsenal are currently in negotiations with Chelsea as they look to strike an agreement over a season-long loan move.
There is a belief that personal terms will not be an issue if the two London rivals can come to a final agreement.
Are Arsenal facing competition?
Sterling is believed to be hugely interested in the chance to join Arsenal, but he could still be given the opportunity to move to an alternative club.
According to Sky Sports News, Chelsea are currently in talks with several clubs over a deal for Sterling before the transfer deadline.
If the Gunners do win the race to sign the winger, he will add valuable strength in depth to Arteta's wide options.
Arsenal's current wide players include Bukayo Saka, Gabriel Martinelli, Leandro Trossard and Reiss Nelson, although the latter could still leave the club before the window closes.