Pucovski was set to make his debut in the first Test after David Warner was ruled out due to a groin injury.
Josh Hazlewood and Pat Cummins shared nine wickets as Australia beat India by eight wickets on Day 3 in Adelaide.
Adelaide Test Virat Kohli looked dejected during post-match presentation after India suffered an eight-wicket defeat at the hands of Australia.
Umesh and Shami also kept things tight although they were a little more on the shorter side during the session compared to Bumrah.
Australia vs India: In a big blow to Australia, David Warner will not be part of the first Test against India in Adelaide after he was ruled out due to a fitness issue.
Pucovski or Burns who should open with Warner in the Test series against India? This is the question that has been doing rounds in the Australian media.
Referring to this period as a silver lining, Burns feels this is a time when people can make themselves strong, from a physical perspective.
Overall, 20 men and 15 women cricketers have been awarded CA contracts.
David Warner and Marnus Labuschagne hit second straight centuries as Australia ended opening day's play at a dominating 302/1.
Test vice-captain David Warner will have the company of either Burns or Bancroft in the first Test starting on November 21 at Brisbane.