Bancroft and Smith have caused a storm by opening up in recent days over the scandal as they re-emerge into public life, with their comments widely interpreted as deflecting all blame onto Warner.
A number of high-profile figures have blasted them for dragging the issue back into the spotlight and detracting from the ongoing third Test against India in Melbourne.
Some believe the relationship between Bancroft and Warner is now untenable while local reports have suggested opposition to Warner remains within the Australian team.
But Finch, the one-day and Twenty20 captain, insisted they would all be welcomed back.
"It's nine months ago and I think in the next three months when Davey and Steve are ready to be allowed to come back and play cricket for Australia and their states I think from my point of view, they'll be welcomed back with open arms," he said.
"I think that whatever has happened has happened," he added.
"The punishment has been dealt. They've been working really hard off the field to meet every criteria and gone above and beyond everything that has been asked of them to come back and play international cricket again."
Finch's support is seen as important after Cricket Australia chief Kevin Roberts was quoted by Sydney's Daily Telegraph as saying he would canvass the dressing room to see if they were wanted.
Smith and Warner were banned for a year from international and domestic cricket for their part in using sandpaper to alter the ball in South Africa in March.
Bancroft was suspended for nine months and is due to make his return this weekend.
Former Australian internationals Ricky Ponting and Dean Jones have both criticised Smith and Bancroft for giving the interviews, and Allan Border also weighed in.
"My personal view is I would have preferred the interviews weren't done," he told Fox Sports.
"They're just rehashing a lot of stuff we already know and what was the point of it all? They could have just admitted they're all responsible for doing the wrong thing."
Bancroft confirmed in his interview that Warner asked him to alter the ball while Smith admitted he failed as a captain by turning a blind eye to what went on.
Warner has not responded to the latest revelations.
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