The 18-year-old, who broke into the Dons’ first team last season and made 33 appearances, will cost £4m up front with the remainder due in appearance-related add-ons.
That £4m fee beats the previous best the Scottish Premiership side received for Scott McKenna when he moved to Nottingham Forest for a reported £3m in September 2020.
Ramsay’s performances last season earned him the Scottish Football Writers’ Young Player of the Year award.
He is likely to travel to Merseyside for a medical later this week.
It is understood manager Jurgen Klopp is a fan of England and Borussia Dortmund midfielder Jude Bellingham but with the German club having already sold one major player in Erling Haaland to Manchester City they will not sanction another departure.