Australia's Test squad took staggered flights to the subcontinent on Tuesday and Wednesday ahead of the first Test that begins in Nagpur on February 9.
AAP understands Khawaja had not been due to fly out until Thursday.
Every member of the 18-man squad has been cleared to enter India bar Pakistan-born Khawaja, who also faced visa challenges when he tried to enter the country in 2011.
On that occasion, Khawaja took to social media to vent his frustration he had not been permitted to enter the country as an Australian because he was not born in Australia.
A Cricket Australia official told AAP the governing body was aware of the situation and was hopeful Khawaja would be approved for entry into India imminently.
This month's tour is set to be Khawaja's first time playing Test cricket in India, but he has been cleared to play in the country in other formats on numerous occasions.
He toured with the Test team in 2013, represented Rising Pune Supergiant in the IPL in 2016, played for Australia A on an Indian tour in 2018, and toured again with the national ODI team in 2019.
Khawaja's Big Bash League side the Brisbane Heat are scheduled to play the Sydney Sixers in 'The Challenger' final at the SCG on Thursday night.Â
But a Heat official told AAP it was unlikely Khawaja would participate in the match if he was still in Sydney, with securing a visa to India remaining the player's top priority.
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