The 19-year-old has been at the Merseyside club since 2022, following his move from his boyhood side, then managed by Ange Postecoglou.
Per The Guardian, Doak is set to complete a £25 million transfer to Bournemouth, which will land Liverpool a £24.4 million profit on the player they signed from Celtic three years ago.
Fabrizio Romano also posted an update on his X account, suggesting that the winger's move to Andoni Iraola's side is getting closer. He said: "Bournemouth are close to getting a deal done for Ben Doak, worth a £25m package.
"Negotiations are at an advanced stage with Liverpool, as the Guardian reports."
Coincidentally, both Liverpool and Bournemouth meet tonight (Friday, August 15), as they kick off their respective Premier League campaigns at Anfield.
Despite being just 16 at the time, Doak made two appearances for Celtic's first team against Dundee United and Rangers, before moving to the Anfield side in the summer of that year.
Doak has made 10 appearances for Liverpool thus far, though he was an unused substitute in last weekend's Community Shield match against Crystal Palace, which the London side won 3-2 on penalties.
Due to a raft of new signings, it would appear that Doak's future lies away from Anfield and Arne Slot.
He spent last season out on loan at Middlesbrough, where he played 24 times under Michael Carrick's Championship side.