The Dutch midfielder, 27, has 12 months left on his current contract.
And he revealed this week he wants to stay. That seemed unlikely when talks broke down in January after De Jong snubbed an offer worth more than £100,000 per week, says The Sun.
But he played a key role in City's title charge and now looks to be given a lifeline.
Boss Roberto Mancini does not plan to buy a central midfielder this summer - meaning De Jong remains part of his plans.