"An MRI exam in Zagreb showed that after some 20 days of therapy the situation with the (right upper arm) injury has improved," 26-year-old Cilic told AFP.
"Since there is very little time for a full recovery and training, my appearance at the Australian Open is unfortunately under a big question mark.
“I have not cancelled my appearance in Melbourne. I will leave it for another seven to eight days to see how the situation will develop," he added.
The Australian Open starts on January 19.