Raheem Sterling has scored 120 goals for Manchester City under Pep Guardiola - only Sergio Aguero (124) has managed more for the club since the manager's arrival in 2016
Sterling, who joined from Liverpool in a £49m deal in 2015 and has scored 131 goals in 339 games, is a major transfer target for new Blues owner Todd Boehly.
It is understood Chelsea are yet to lodge a formal bid for the 27-year-old, but one is expected shortly.
Sterling has a year left on his contract and is understood to be reviewing his options.
Sterling, who has 77 England caps, has never made any secret of his desire to play as much as possible and be a central figure in a team that challenges for major honours.
He could be the Blues first major signing since they were taken over by a consortium led by Boehly in May.
Chelsea are looking to boost their attacking ranks after allowing Belgium striker Romelu Lukaku to rejoin Inter Milan on a season-long loan.
Since Pep Guardiola became manager in 2016, only Sergio Aguero (124) has scored more goals for City than Sterling (120).
Sterling scored 13 goals in 30 Premier League appearances last season as he won his fourth league title and ninth major honour in seven seasons with City.
However, he was on the bench for both legs of the Champions League semi-final defeat by Real Madrid and the epic final game of the season against Aston Villa.
Sterling did spark the memorable last-day league title success by coming on to set up Ilkay Gundogan's crucial first goal as City came back from 2-0 down to win 3-2 and pip Liverpool by a point.
Of City's attacking players, only Bernardo Silva started significantly more Premier League games last season - 33 to Sterling's 23.
Phil Foden started one more and £100m man Jack Grealish one fewer.
But Erling Haaland's summer arrival from Borussia Dortmund appears to change the dynamic, with the Norwegian likely to be a starter, especially in the biggest games.
Argentina forward Julian Alvarez will also be arriving at the Etihad this summer from River Plate after a deal was agreed in January.
-- Courtesy of BBC Sport