Ramsay is highly-rated at Aberdeen with the teenager putting in a raft of impressive performances in the first of last season. An injury saw him miss a chunk of the campaign and he struggled to hit the heights of his early displays on a consistent basis when he returned.
Clubs from England, including Leeds United, and abroad have shown an interest but Liverpool are at the front of the queue.
On Sunday, transfer specialist Fabrizio Romano reported talks were ongoing with Aberdeen demanding €10million with add ons.
According to the Press and Journal, the Dons have put their valuation at £5million up front with a further £5million via add ons and clauses.
Such a sale would smash the club’s record transfer sale which took Scott McKenna to Nottingham Forest for £3million plus add ons, one of which was £1million for promotion to the Premier League.
Liverpool are on the verge of breaking their own transfer record having agreed a €100million with Benfica for the signing of Uruguayan forward Darwin Nunez.
Ramsay is viewed as back-up to Trent Alexander-Arnold and the signing of the Scotland Under-21 international would be viewed as low risk.
For Aberdeen, the money would be hugely significant with Jim Goodwin trying to overhaul the squad after a tenth place finish, while the club are looking to build a new stadium.