Press Association Sport understands the 19-year-old, who impressed at the World Cup, met with Reds officials and manager Brendan Rodgers at the club's Melwood training ground on Wednesday but negotiations are continuing and as yet no medical has been scheduled.
A fee, believed to amount to about £10 million in total, has already been agreed with his club Lille but a reported approach from Tottenham may yet prove a stumbling block.
However, Liverpool's interest has been long-standing and they remain in pole position to secure the services of the talented youngster.
Origi was non-committal on his future when asked during an event in his home town of Houthalen-Helchteren staged to recognise his performances in Brazil.
"I myself am still thinking about it," he told reporters.
"It is true that there are offers from all over Europe. Now I have to look carefully where I will grow as a player and as a person.
"I think things will be clearer within two weeks at the most."
The transfer of Benfica winger Lazar Markovic is much more advanced with the Serbia international expected on Merseyside in the next 36 hours - and possibly as early as Thursday - to finalise his move.
Having triggered the 20-year-old's release clause of £20 million Markovic is heading to Merseyside for a medical and is likely to become manager Rodgers' fourth signing of the summer after Southampton duo Rickie Lambert and Adam Lallana and Bayer Leverkusen's Emre Can.
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