The Reds stole a march on Tottenham and Manchester United to agree a deal which will see them pay an initial £37.5million with a maximum of £12.5m in add-ons if the 25-year-old is hugely successful at the club.
Diaz was manager Jurgen Klopp's first choice for a summer transfer but growing interest, specifically from United, forced them to move early.
PA Sport says they will have people on the ground in Argentina when Diaz, who is set to play against Peru at home on Friday evening, arrives for Tuesday's World Cup qualifier in order to expedite proceedings.
However, there still remain significant hurdles to overcome, with a medical still a logistical issue as they have to be granted access to the player in between the two internationals and in enough time to be able to complete a deal before Monday's deadline.
Should the deal come off – and the club remain cautious about that prospect – it would be a huge coup for Julian Ward, who succeeds sporting director Michael Edwards in the summer, as this is the first transfer he has taken the lead on using Edwards' previously implemented strategy.
Liverpool had to move earlier than anticipated after learning of United's plans for Diaz.
It is believed the Red Devils' interim manager Ralf Rangnick had expressed a significant interest in bringing the player to Old Trafford and that sparked their arch-rivals into action.
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