The Scottish giants are ready to meet the Reds’ asking price for the 22-year-old, who has been desperate to make a return to Ibrox this summer.
Kent starred on loan with Rangers last season, making 43 appearances and winning the Scottish Young Player of the Year award for his performances.
A host of clubs – Rangers included – were keen to take the wideman on loan during this transfer window, but Liverpool made it clear to the player that a temporary move, which would have been the sixth of his career, would be of no benefit.
Kent featured for Jurgen Klopp’s first-team in pre-season, but has began the campaign proper with Neil Critchley’s Under-23s.
Leeds United were interested in a permanent deal last month, but baulked at the Reds’ demands and backed away.
Interest from Brugge emerged in recent weeks, and the Belgians were ready to pay up to £6m to take him to Jan Breydel Stadium.
But Rangers have now put together a package that Liverpool have deemed acceptable, and Kent is expected to travel to Glasgow to complete a medical and finalise personal terms. Liverpool are also likely to negotiate a sell-on clause.
Kent’s will not be the only departure at Anfield on deadline day, with teenage striker Bobby Duncan set to complete a €2m switch to Fiorentina following his public row with the club last week.
Duncan, via his representative Saif Rubie, released an explosive statement in which the Reds were accused of “mentally bullying” and “destroying the life” of the 18-year-old, who was keen to leave the club in search of first-team football.
The striker, who is the cousin of Kop legend Steven Gerrard, is set to pen a three-year deal with Fiorentina, while Liverpool will receive 20 per cent of any future transfer fee. He will leave Anfield with the club’s best wishes, despite last week’s public spat.