The 30-year-old player is one of several Chelsea players expected to leave the team this summer, following a disappointing loan spell at Arsenal last season.
During his 28 games for Arsenal, Sterling scored only one goal and provided five assists, which may have contributed to his potential departure.
West Ham United has expressed interest in signing Sterling, and his former manager Graham Potter is reportedly supporting this move.
Potter, who managed Sterling during his time at Chelsea, still maintains a good relationship with the player, which may have facilitated this potential transfer.
Fulham, another London-based club, is also interested in signing Sterling, although no official offer has been made at this time.