City boss Mark Hughes hopes to secure the defender to a new deal this week.
The Manchester Evening News says if Dunne puts pen to paper on a new long-term deal when he returns for pre-season training next week.
It will represent a massive U-turn for the player who said he had played his last game for the club.
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Four weeks ago Dunne travelled to Tottenham for talks, but the deal was stopped because City sacked the manager.