While the Blues are currently well stocked for options in the final third, head coach Thomas Tuchel has been left frustrated by the amount of chances which have been wasted this season.
According to The Telegraph, selling at least one of Christian Pulisic, Hakim Ziyech and Timo Werner is a possibility over the coming months.
The report adds that Chelsea may use any funds generated from such sales to launch a bid for Sterling, who has just one year left on his Man City contract.
Although the Premier League champions will not want to sell to a rival, a bid in the region of £50m may prove too hard to turn down in the current climate.
Sterling, now 27 years of age, has spent his professional career in the North-West, but he lived in London until 15 when he was a part of Queens Park Rangers' youth setup.
Real Madrid are also said to be monitoring the situation having missed out on the signing of Kylian Mbappe.