Mancini is reportedly annoyed with Brian Marwood, Football Administration Officer, for not getting van Persie's signature earlier.
The Italian was hoping to have van Persie before Manchester City started their tour of China.
Arsenal and Manchester City will be playing each other on Friday in Beijing.
The City boss has been told that he has to reduce the clubs' wage bill by offloading one other forward; Edin Dzeko, Emmanuel Adebayor or Carlos Tevez.
City have only offered £15 million for the Dutch striker, the highest bid so far, but Arsenal released a statement saying they would not be listening to offers under £20 million.