The 18-year-old and his representatives are believed to have been in advanced talks with the Reds this month over a proposed move to Anfield.
Despite one report claiming that Liverpool had agreed a £4m fee with Aberdeen, Sky Sports News claims that the Dons are demanding £10m for Ramsey and want to receive at least £5m up front with a further £5m in add-ons.
Aberdeen's record sale is only £3m when they let defender Scott McKenna join Nottingham Forest in 2020, and the Scottish Premiership outfit have since received an extra £1m following the latter's promotion to the Premier League.
Ramsey is highly regarded by Aberdeen after he enjoyed a breakthrough 2021-22 campaign, which saw him win the Scottish Football Writers' Young Player of the Year award.
Liverpool are not the only club interested in signing Ramsey, with other teams in England, Germany and Italy keeping tabs on his situation, but it is thought that the teenager would prefer a move to Anfield.
Ramsey, who scored once and registered nine assists in 33 games across all competitions last season, has two years remaining on his Aberdeen contract.