The substantial bid falls significantly short of the £35 million valuation placed on the academy product by the Merseyside club this summer.
Anfield officials are entirely unwilling to sanction a cut-price departure for the 25 year-old despite his delicate contract situation with the Premier League side.
The English midfielder currently has just one remaining twelve-month period left on his existing professional contract with his boyhood club.
This approach represents the second time that the reigning Italian champions have attempted to lure the player away from England this calendar year.
The Serie A outfit previously expressed serious interest during the January transfer window by proposing an initial loan deal containing an option to buy.
Inter Milan sporting director Piero Ausilio publicly confirmed their ongoing pursuit of the player by stating that they are paying close attention to his developments.
Ausilio added that the club has not hidden their admiration for the player and clearly understand how the situation could unfold in the coming weeks.
Italy forward Federico Chiesa revealed that the English midfielder had actively inquired about the realities of living in Italy during recent conversations.
Federico Chiesa told a local sports newspaper that the midfielder was curious about the lifestyle transition as interest from the continent intensified.
The homegrown talent originally joined the celebrated youth ranks at Anfield at nine years old before graduating to sign his first professional contract.
He has since established himself as a reliable squad player under successive managers but must now decide whether to commit his long-term future to the club.
The midfield player faces intense competition for starting places next season and may look to force a move if regular first-team assurances are not provided.
Liverpool intend to stand firm on their valuation as negotiations continue over the coming weeks.