However, the England international will enter the final year of his existing deal at the end of the current season.
ESPN says City are keen to resolve the issue before the end of the campaign.
There had been some doubt earlier in the season whether Sterling would decide to prolong his stay at the Etihad Stadium past 2023.
He had become frustrated after he had lost his place as a regular starter for Pep Guardiola's side.
But in recent months though Sterling has become a regular part of the City team, starting ten of their last 12 league outings.
Sterling was also voted December's Player of the Month after netting five goals in four games.
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