Gilchrist says Carey, the South Australian who made his international debut last summer, was a "superstar" who should be given the gloves for Australia's limited-overs tour of the UK next month ahead of their World Cup defence next year.
Tim Paine, who was elevated to the Test captaincy after the ball-tampering scandal in South Africa, is technically Australia's incumbent ODI keeper having taken over from Matthew Wade for the series against England last January.
Carey stepped in for one match in that England series when Paine was ill and Gilchrist says he's seen enough already to be sure the 26-year-old can handle the job full-time.
"It looked like the most smooth transition to international cricket that I can remember for a long time," Gilchrist told Fox Sports of Carey's debut in Brisbane.
"He played that one-day match up at the Gabba and looked like he belonged there. He's a superstar.
"I think he has to play in the 50-over format and that will allow Tim Paine to carry out this role, this extra responsibility that he has in Test cricket."
Carey, who also played all matches in Australia's unbeaten T20 tri-series campaign last February, was a new addition to Cricket Australia's central contract list that was announced in April, indicating selectors already have him in mind for higher honours this year.
Carey pushed himself onto the selectors' radar with a breakout KFC BBL campaign last summer, where he was the tournament's second-leading run-scorer. He also averaged 38 in the JLT Sheffield Shield, including his maiden first-class hundred, and averaged 33 as an opener in one-day cricket for South Australia.
And Gilchrist says the left-hander's glovework is also up to international standard.
"He's a gun, he's a gun in all facets," Gilchrist said.
"He's a very, very capable gloveman. He's very athletic and strong ... he's fit, he's a terrific young man and he bats beautifully, too. We saw that in the Big Bash were he dominated throughout and performed well."
Australia are set to announce Steve Smith's replacement as one-day captain in the coming weeks and Finch, part of the 2015 World Cup-winning side, has emerged as a leading contender for the role.
While some former players have questioned the wisdom of making a wicketkeeper like Paine Test skipper, Gilchrist pointed to Indian legend MS Dhoni as an example of a gloveman who has handled the triple responsibility of keeping, batting and captaining at Test level.
But the 46-year-old said Paine shouldn't be part of the one-day team moving forward.
"Tim Paine is right to do that (in the Test team), but I think Finch should and would captain the one-day team for the moment and Carey should play."