Djokovic, one of the most high-profile athletes unvaccinated against COVID, said last week he was hoping for a positive outcome shortly after applying to enter the U.S. to compete in ATP Masters 1000 events in Indian Wells and Miami this month.
"Novak Djokovic is one the greatest champions our sport has ever seen," the U.S. Open Twitter account said on Friday.
"The USTA and U.S. Open are hopeful that Novak is successful in his petition to enter the country, and that the fans will be able to see him back in action at Indian Wells and Miami," it added.
The U.S. vaccine requirement for foreign air travellers is not expected to be lifted before the main draw begins at Indian Wells on March 9th and the Miami Open later in the month, meaning Djokovic could miss out for a second straight year.
U.S. President Joe Biden's administration said in January it would lift COVID emergency declarations on May 11th, but Djokovic - named on the Indian Wells entry list - said he had submitted the required documentation for special permission.
Indian Wells tournament director Tommy Haas said in January it would be a "disgrace" if Djokovic was not allowed to compete this year after the Serbian also missed last year's U.S. Open.
Djokovic, who missed last year's Australian Open and was deported from the country due to his vaccination status, has said he would skip Grand Slams rather than have a COVID shot.
The 35-year-old won a record-extending 10th Australian Open title and his 22nd Grand Slam in January.