Australian Prime Minister Scott Morrison has left the door open for Novak Djokovic to return to the country sooner than initially anticipated.

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The men's tennis world number one was deported on Sunday after losing a visa battle to remain in Australia.

Under Australia's immigration laws, Djokovic cannot be granted another visa for three years.

However, Mr Morrison said Djokovic could be allowed entry into Australia sooner under the "right circumstances."

This would potentially allow him to take part in the Australian Open next year,

The tournament, which has been overshadowed by the unvaccinated player's visa troubles, began in Melbourne on Monday with Germany's Tatjana Maria taking on Greece's Maria Sakkari.

Djokovic had also originally been scheduled to play on Monday.

Australian law provides for compelling or compassionate reasons for the three-year visa ban to be waived. If the exemption is granted, it means Djokovic could compete in the next Australian Open.

"I'm not going to pre-condition any of that or say anything that would not enable the (Immigration) minister to make the various calls he has to make," Mr Morrison told Australian radio station 2GB earlier on Monday morning.

"(The ban) does go over a three-year period, but there is the opportunity to return in the right circumstances, and that will be considered at the time."