Dunne would therefore be available on a free transfer next summer so City could cash in while they can, with Spurs thought to be leading the race.
Newcastle and West Ham are also reported to be interested in the 28-year-old Republic of Ireland international, who is rated at £5m.
Dunne played for the Republic in a 1-1 draw against Serbia last Saturday and their 1-0 win over Colombia at Craven Cottage onThursday.
His departure could be the first of several high-profile transfers from City this summer with the future of Blues boss Sven-Goran Eriksson still up in the air.