The Athletic says the pair's poor fitness record has convinced City to move them out this summer.
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Stones is off contract in June, while Ake is now inside the final 18 months of his deal.
Ake turned down a move to West Ham last week and is also interesting Crystal Palace. However, he is likely to see out the season before departing.
City are in the process of rebuilding their defensive options, with Crystal Palace captain Marc Guehi a target this January.