The England hero currently makes £175,000 a week at the Etihad.
And the Times claim talks between Sterling's men and City chiefs are due to resume in the next few days.
Sterling is not pushing for a move away from City but wants to earn the same as the club's best paid player, Kevin De Bruyne.
City are said to be mindful of Financial Fair Play and will incentivise the deal heavily.
De Bruyne signed a new deal in January that lasts until 2023 and, when bonuses are included, he makes £342,000 a week.
That includes bonuses, image rights and a signing-on fee spread over the duration of his contract.
Sterling signing a new deal would be the latest in a trend at the Etihad.
David Silva – who says he wants to leave the club in 2020 – Fernandinho, Gabriel Jesus and Ederson all put pen to paper recently.
City have made an offer to the former Liverpool man but with the main increases in pay delayed until 2019-20 and 2020-21, according to the Times.
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