Milan lost 2-1 at Sampdoria to an injury-time goal on Sunday to all but end their Serie A title hopes while media have been rife with rumours that the rookie coach is unhappy with club president Silvio Berlusconi for his thrifty transfer spending.
"There are no problems over buys, it's just that he has three kids in Rio and sooner or later he will go back to Brazil," Galliani told Sky television.
"But I think I can convince him to stay in Italy."
Leonardo, who had no previous coaching experience but has charmed the football world with his eloquence in five foreign languages, took over after Carlo Ancelotti left for Chelsea at the end of last season.
The 40-year-old was seen by Milan fans as a cheap gamble and their big defeat by Manchester United in the Champions League last 16 last month prompted speculation about his future as the Rossoneri keep quiet about the details of his contract.
Galliani also flatly denied media reports that Italy coach and former Juventus and Inter Milan boss Marcello Lippi would become Milan's sporting director after the World Cup.
