The Reds triggered the Japan international's release clause last week, just a couple of days after facing him for the second time in the Champions League group stage.
Providing no problems are encountered the 24-year-old will become a Liverpool player on January 1, it is now understood.
It is anticipated Minamino would go straight into Jurgen Klopp's squad and could be available for the FA Cup third round tie at home to Everton four days later.
The deal is viewed by Liverpool as outstandingly good value as they believe the player's market value is three times what they are paying for him.
But having kept tabs on him since 2013, sporting director Michael Edwards and his recruitment team became aware of his release clause and acted quickly when interest was expressed from Manchester United, Borussia Monchengladbach and AC Milan.
Minamino, who impressed in his two Champions League outings against the Reds, has scored nine times in 22 appearances this season.
Meanwhile, defenders Ki-Jana Hoever and Sepp Van Den Berg, and goalkeeper Caoimhin Kelleher, are all flying out to join Liverpool's senior squad in Qatar.
However, it's being reported that Harvey Elliott, who impressed in the 5-0 Carabao Cup defeat at Aston Villa as part of the youngest team in the club's history on Tuesday, will not be making the trip.
After 20 senior players flew out on Sunday only three places were left available, one of which had to be a goalkeeper as Liverpool are obligated to name three in their Club World Cup squad.
With only two fit first-team centre-backs in Virgil Van Dijk and Joe Gomez, Hoever, who came off with cramp against Villa but has been passed fit, and Van Den Berg will provide some cover for Jurgen Klopp if necessary.
Liverpool play their semi-final against Mexican side Monterrey on Wednesday evening.