Genoa are looking to reduce their wage bill and rehaul their squad in the coming months and the 31-year-old is likely to leave the Serie A side to achieve that aim.
Former Italy coach Marcello Lippi has been coach of Guangzhou Evergrande since 2012, and is keen on bringing Gilardino to China.
Preziosi is unsure if the 57-time Italy international will accept Lippi’s offer but is hopeful that the striker will agree to a move abroad.
"We don't know whether Gilardino will accept or not," Preziosi told Telenord on Wednesday.
"If he doesn't, then we will keep him and continue to give him a great deal of money. If he doesn't then we already have some alternatives.
"We want to bring the average age of the squad down and re-invest the money for a younger forward who we believe could be as strong as Gilardino."
Gilardino scored 12 goals in 26 league games for the Serie A side last season having spent the previous campaign on loan at Bologna.