Shami has not played for India since his appearance in the 2023 World Cup final.
According to the report, Shami's playing kit has already headed Down Under and the fitness clearance from the NCA's medical team remains a "matter of formality".
While the Gabba Test (from December 14) could be touch and go for Shami, it is certain that he will compete in the Boxing Day (December 26) Test at MCG.
"Shami's India kit has already been dispatched to Australia. He will complete Mushtaq Ali Trophy T20 assignment and then leave," PTI quoted a source as saying.
Shami has not played for India since his appearance in the ODI World Cup final in November last year. The right-arm quick underwent an operation on his Achilles tendon earlier this year, and then had an extended rehabilitation at the National Cricket Academy (NCA) in Bengaluru.
The 34-year-old was supposed to make his comeback in the home Test series against New Zealand but he developed swelling in the knee, causing delay to his return.
Since the knockout round of Syed Mushtaq Ali trophy is taking place in Bengaluru, it is expected that the NCA medical team head Dr Nitin Patel and Strength and Conditioning trainer Nishant Bordoloi would be assessing Shami after Bengal finishes its campaign.
"Shami will be playing the pre-quarter final for us against Chandigarh. He will join us in Bengaluru by tomorrow. However, I am not sure if he will be available if we qualify for quarters or go the distance. Guess he will be fit and available for last two Australia Tests," Bengal head coach Laxmi Ratan Shukla told PTI.
Shukla endorsed the views of former India head coach Ravi Shastri, who believes Shami is needed as early as possible in Australia.
"He has already shed around six kilograms of body weight. He has played seven T20 games in 13 days. If he plays pre-quarters it will be eight games in 16 days.
"Shami himself wanted to play fair amount of domestic cricket and inform NCA how his body reacts," Shukla said.
Having won the first Test in Perth, Team India are leading the five-match Border-Gavaskar Trophy 1-0. The second night is currently in progress at the Adelaide Oval.
(With PTI Inputs)