India captain Virat Kohli is facing calls to hand over some of his leadership duties to Rohit Sharma after another missed opportunity in the Indian Premier League.

Sharma led the Mumbai Indians Tuesday to a fifth IPL title -- something that has eluded Kohli in the 13 editions of the tournament -- prompting calls for him to take over the captaincy of the national T20 side.

India leave for Australia this week to begin a two-week coronavirus quarantine before playing three T20s, three one-day internationals and four Tests.

Following the IPL final, former India batsman Gautam Gambhir and ex-England captain Michael Vaughan said Sharma should take over as the national T20 captain.

"Rohit has won five IPL titles; he is the most successful captain in the history of the tournament," Gambhir told ESPNcricinfo. "Going forward, it'll be a shame if he doesn't get India's white-ball (one-day) or just T20 captaincy."

Sharma has transformed Mumbai since taking over the captaincy from Australian great Ricky Ponting in 2013, and all five of their titles have come under his leadership.

Kohli's Bangalore, however, bowed out in the playoffs this season -- after two bottom-placed finishes in the previous three editions.

Vaughan also backed Sharma to become India's T20 leader. "Without question Rohit Sharma should be the Indian T20 captain," he wrote on Twitter, describing him as a "fantastic man manager and leader".

"He knows exactly how to win T20 games. It would also give Virat a chance to take a breather and just be the player."

Vaughan said relieving Kohli of the captaincy was not "an admittance of failure", but rather "what is best for the Indian cricket team".

Sharma is not included in India's one-day and T20 teams for Australia as he is recovering from a hamstring injury that saw him a miss several IPL games.

The 33-year-old will be part of the four Tests, however, while Kohli will miss three of them as he is taking paternity leave after the opening match in Adelaide.