Buttler played under Gill's captaincy in the IPL this year, with his Gujarat Titans (GT) side qualifying for the playoffs and both men scoring more than 500 runs each in the campaign. Speaking on For the Love of Cricket, his new podcast with Stuart Broad, Buttler said that Gill will be "his own man" while combining the best traits of his two predecessors.
"He's a really impressive player and an impressive young man," Buttler said. "He's pretty calm and measured when he speaks, but [it's] interesting, I feel like on the field he's got a bit of fight about him; a bit of intensity, quite passionate. I think he'll be a mix of Kohli and Rohit.
"Kohli [was] that sort of real aggressive [character], really transformed the Indian team, in your face, up for the contest. Rohit [was] a bit on the other side, a bit more laid back, very cool, calm, collected customer, but with that sort of fight. I feel like, from my time knowing Shubman so far, he'll be a bit in the middle. He's obviously learned from those two guys… but he'll be very much his own man."
Buttler has spent more time in India than any other England player of his era, and said it is hard for English fans to comprehend the "stardom" of India's best players. He predicted that one of Gill's biggest challenges will be to ensure that he does not let the captaincy affect his batting - as happened with Buttler towards the end of his England's white-ball captaincy.
"He talked about compartmentalising batting and captaining; so when he's batting he just wants to be a batter, and then he will try and work on his captaincy and try and separate the two roles," Butler said. "When you're doing such a big job as being captain of the Indian cricket team, he'll have to try and do that well and have some good people supporting him.
"I don't think we can quite understand the level of interest and the stardom that these guys have. You see it around the IPL, you're aware of it, but actually living that yourself… I think they say the Indian Test captain is like the third or fourth-most influential person in India, behind the Prime Minister etc. - so you really are put up on that pedestal.
"It's going to be a huge job for him. He's obviously captained two seasons of IPL cricket, which is a big, pressurised job and he's sort of the prince. Kohli is the king, Shubman is the prince: that's the narrative that they spin out there, and I feel that he's the coming man… Stepping into that No. 4, it's big shoes, isn't it? Coming behind Virat, and Sachin Tendulkar before that as well. That's obviously a huge role."
India's tour of England will begin with the first Test in Leeds from June 20.