Nicholas has since stepped in as a drummer at Collins' solo shows - and his presence helped inspire the Genesis reunion, Banks said.
"He can sound like Phil and it gave us a whole idea of how we could do it, because we knew Phil couldn't be the drummer on the road again," the keyboard player said.
Image copyrightGetty ImagesImage captionBanks, Collins and Rutherford pictured in 1987
The veteran band, whose hits include Land of Confusion and I Can't Dance, will kick off their Last Domino? tour in Dublin on 16 November.
They will also play shows in Liverpool, Leeds, Birmingham, Belfast, Manchester, Newcastle and Glasgow, as well as two nights at London's O2 Arena.
"I'm looking forward to doing it," said Rutherford. "I worked it out and we've only done two shows in the UK in the last 28 years, so we haven't over-worked it."
Missing members
Founding member Peter Gabriel, who left the group in 1975, will not be taking part. Guitarist Steve Hackett will also miss the shows.
"Peter left the band 45 years ago and he's been trying to live it down ever since," said Banks.
"When they put his birthday in The Times, they always say, 'Peter Gabriel - Genesis singer.' And I think, 'What's the guy been doing since then, for God's sake?'"
Banks said it wouldn't make sense to bring Gabriel back because "most of the songs people know" came after his departure, but added: "We love Peter."
Collins, whose voice was croaky after a recent illness, said the set list was still coming together.
"There are songs that you feel you have to play because the audience would feel cheated if you didn't," he told Ball.
"There are a few old dogs that won't be running," he added, saying songs that were "based more on my drumming" would be dropped.
The singer arrived at Radio 2 with a walking stick, which he has used since a back operation in 2015 left him with drop foot.
Rumours of a reunion had been circulating since Collins and Rutherford performed together in Berlin last June.
Earlier this week, a photograph of the three members appeared on Genesis's official Instagram account with the caption: "And then there were three."
100 million albums
Genesis started life as a progressive rock band in the 1970s, but after a series of line-up changes, they transformed their sound and became one of the most successful mainstream rock bands of the 80s.
They recorded 15 studio and six live albums, selling more than 100 million records, while scoring top 20 hits with songs like Invisible Touch, Turn It On Again and In Too Deep.
The band last played together in 2007 to mark the 40th anniversary of their formation at Charterhouse School in Surrey.
Those shows mixed their hits with the more expansive, experimental material from 70s albums like Selling England By The Pound and The Lamb Lies Down On Broadway.
Image captionThe band announced their reunion live on BBC Radio 2
Collins announced his retirement in 2011 after nerve damage left him unable to play the drums, but he returned to the stage in 2016 following his back operation.
That prompted speculation that Genesis might later reform, but Banks shot down speculation in 2018, saying that "getting everybody in the same place at the same time is impossible".
Speaking on Wednesday, the musician said Collins' live comeback had been the catalyst for their reformation.
"Phil's been out on tour for the last two-and-a-half years and it seemed the natural moment to have a conversation about it," he said.
This website uses cookies so that we can provide you with the best user experience possible. Cookie information is stored in your browser and performs functions such as recognising you when you return to our website and helping our team to understand which sections of the website you find most interesting and useful.
Strictly Necessary Cookies
Strictly Necessary Cookie should be enabled at all times so that we can save your preferences for cookie settings.
If you disable this cookie, we will not be able to save your preferences. This means that every time you visit this website you will need to enable or disable cookies again.