The clubs are still in negotiations over an agreement that will include a ??12.5m up-front transfer fee and additional payments based on certain conditions that would eventually be met by the player.
Clyne, 24, is expected to undergo a medical next week after returning from holiday and is set to become the direct replacement for Glen Johnson, who was released by the club when his contract expired earlier this month.
His signing is not expected to have an initial impact on recent signing Joe Gomez, a young right-back who joined from Charlton and will feature for Liverpool pre-season, although sources understand a possible loan back out of Anfield is a possibility.
Sky Sports??reported earlier this month that Liverpool had seen a????10m bid for Clyne rejected by Saints. Clyne has a year left on his Southampton deal and has been stalling over a new contract amid reported interest from the Reds’ north-west rivals Manchester United.
Clyne joined Southampton from Crystal Palace in 2012 and made 41 appearances for Ronald Koeman???s team last term, earning his first England cap in November.
He played the full 90 minutes in a 3-1 European qualifying victory over Slovenia, and has gone on to make four international appearances.
Liverpool have been swift in their transfer dealings so far in the current window, landing Danny Ings and James Milner on free transfers as well as young Brazilian attacker Roberto Firmino.
They also signed three players from Southampton last summer; Rickie Lambert, Adam Lallana and Dejan Lovren.