Instead, they'll appear as holograms, with a studio reportedly being purpose-built to house the production for a May opening date.
Ulvaeus said in a recent BBC interview that the virtual reunion could "hint at another ending, a happy ending perhaps", after the band split amid tension in 1982.
He said the band had met in person "with masks and tests and whatever", to work on the album together.
The former bandmates have been working on songs for years now. They announced in 2018 that they had recorded two new tracks, I Still Have Faith In You and Don't Shut Me Down.
Working on plans for the hologram show inspired them to make music together, an "unexpected consequence", they said.
"We all four felt that, after some 35 years, it could be fun to join forces again and go into the recording studio. So we did. And it was like time stood still and that we only had been away on a short holiday. An extremely joyful experience!"
The band's greatest hits collection, Gold, is the second biggest-selling album of all time in the UK after Queen's greatest hits, overtaking The Beatles Sgt Pepper's Lonely Hearts Club Band years ago.
They were offered $1 billion to reunite around 20 years ago, but they refused.
Faltskog said later, "We said no because they wanted 250 shows or something, it was incredible. No chance."
Meanwhile Andersson admitted, "It was a hell of a lot of money to say no to, but we decided it wasn't for us."
