Giovani has scored five goals in his last five games for the Galaxy, who have enjoyed a superb run of eight games straight without a defeat.
"Based on his good form and goals scored for his club, Giovani was invited for this call up. The same Giovani declined our invitation," Osorio confirmed.
Osorio did not specify why Giovani declined the invitation, but the 27-year-old forward last played for Mexico in June 2015 and had not been picked since.
In spite of his declination,Osorio said Giovani and Carlos Vela, who was also another big absentee in Mexico's 23-man roster, have the door open for future call ups.
Giovani is likely to feature for the Galaxy in their Cali Clasico clash against the San Jose Earthquakes at the StubHub Center on Sunday.