The Italy international is rumoured to be unhappy with his current pay packet at Udinese and is looking for an escape route.
Di Natale is under contract until 2012 and his future could become clearer after Italy's friendly with Hungary on Wednesday night.
The forward's agent Bruno Carpeggiani plans to meet Udinese general director Pietro Leonardi on Thursday after a proposed meeting last week was cancelled.
City boss Sven Goran Eriksson is in the market for a new striker after losing recent signing Valeri Bojinov to a long-term injury.
Eriksson also revealed over the weekend that he could raid Italian football again for another player, although Bolton Wanderers hit-man, and former City front man, Nicolas Anelka has been mooted for a move.