The 19-year-old striker has risen to prominence in recent weeks after firing a vital goal for his nation against Russia to help them book a spot in the last 16 of the competition.
Prior to the tournament the teenager had been attracting much interest due to his fledgling showings for Lille in Ligue 1 – he netted five goals last term.
Spurs and Arsenal have been heavily linked with swoops in recent days, but now it is understood that Liverpool have beaten their rivals.
Despite having snapped up Rickie Lambert from Southampton, Brendan Rodgers is thought to be keen to further bolster his attacking ranks, and sees Origi as a good man to have as back-up to Daniel Sturridge and Luis Suarez.
But he may also be sent back to Lille on loan next term to gain experience.
Origi could follow Adam Lallana to Anfield, with various reports indicating that a deal for the England international is close to completion.