The US vaccine requirement for foreign air travellers is not expected to be lifted before main draw action at Indian Wells kicks off on March 9. The Miami Open runs from March 22 to April 2.
World number one Djokovic was named this week on the entry list for Indian Wells, where he is a five-time champion.
"Novak has to obtain special permission as the US is still denying entry to non-vaccinated persons, which is simply unbelievable as the whole world is open and sports events feature vaccinated and non-vaccinated athletes alike," Djordje told Serbian news agency Tanjug.
"Novak has submitted all the required documentation and a request, and the directors of the Indian Wells and Miami tournaments have publicly said Novak is needed at those tournaments and that they want him to come.
"There are only a few days to go before a decision is made and what remains for us to do is hope for a positive outcome."
Last month, Indian Wells tournament director Tommy Haas said it would be a "disgrace" if Djokovic was not allowed to compete at Indian Wells and other tournaments in the United States this year.
Djokovic missed last year's Australian Open and was deported from the country due to his vaccine status. He regained entry into the tournament this year and won it to claim a record-tying 22nd Grand Slam title.
He has previously said he would miss Grand Slams rather than receive a COVID-19 vaccine.
