The Liverpool Echo says the process is progressing well and the Reds should get their man ahead of Monday's transfer deadline.
Liverpool sent a club delegation to Argentina to meet up with Diaz while he is on international duty.
Medical tests are taking place as Diaz prepares for Colombia's next assignment.
Argentina host his side at 11.30pm UK time on Tuesday.
If all goes to plan, it is possible Diaz will be able to travel to Liverpool towards the end of next week.
The 25-year-old Porto winger had been identified by Jurgen Klopp as a first-choice option for summer 2022.
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