The 31-year-old's call comes in the wake of his retirement from the form following intense public scrutiny surrounding his form with the bat.
While Finch has thrown his weight behind his long-term opening partner to pick up his reins, it comes as Test captain Pat Cummins refused to extinguish speculation that he could act as the Victorian's successor.
Australian selectors are currently stuck between the proverbial rock and hard place in their search for the next 50-over skipper given the past misdeeds of several candidates.
As the ringleader of 'Sandpapergate', Warner earned himself a lifetime leadership ban following the fallout of the 2018 incident in the Rainbow Nation. The sobbing Steve Smith was also handed a two-year suspension from holding any official post.
Still, when quizzed about whether he would like to see Warner gifted a reprieve and the armband, Finch spoke openly, unbridled from the shackles of his role.
“I think CA (Cricket Australia) I think are revisiting what that looks like. He’s someone I’ve played under a few times for Australia when he’s had the opportunity to captain, and he’s been fantastic. He’s an unbelievable tactical captain and someone who at the time the guys loved playing under,” Finch said on Triple M radio.
“I’m not 100 per cent sure of what CA’s position is on it. But would I like to see it overturned?
“(Yes) … he’s someone who, you do your time and he’s well and truly done that I think.”
Prior to being pressed by Finch's frame, CA chairperson Lachlan Henderson expressed that dialogue with Warner would need to be opened before any alterations could be made.
“The ban on David being appointed to a leadership position in Australian cricket remains in place,” Henderson wrote in an official statement.
The recently anointed head made mention of Warner's decision to opt out of chasing Asian franchise riches in an effort to restump Australia's faltering domestic T20 competition.
“David has shown strong leadership both on and off field in recent seasons and his decision to play in the BBL (the Big Bash League) for the next two years reflects his ongoing commitment to cricket in Australia," Henderson added.
“The CA Board welcomes David’s wish to discuss his leadership status with directors and this will be arranged at a convenient time for both parties.”
It is not yet known whether Warner will be given the green light to lead the Sydney Thunder throughout the meandering tournament.
While Cummins expressed that "nothing was off the table" in regards to leading his nation across multiple formats, Finch professed that staying on task during abbreviated contests could be too stiff of a drink for the unflappable seamer to stir.
“I think (Smith) captained a Test match in Adelaide after Pat was out with Covid, so I think that’s all been put to bed," Finch continued.
“I think it’s pretty hard (for a fast bowler) but if anyone can manage it, it would be Pat.”