The trio are expected to join the Anfield club in the coming days as Brendan Rodgers looks to fine tune his squad, with Luis Suarez about to join Barcelona in an 88 million euro deal.
Belgium forward Origi, who shot to prominence with his performances at the World Cup, arrived at Melwood on Wednesday for talks over a switch to Anfield from French club Lille.
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Goal understands the 19-year-old attacker was shown around the club's training complex and agreed personal terms, with Tottenham's reported late interest in the talented striker wide of the mark.
Benfica winger Markovic, meanwhile, is expected to fly to England to undergo a medical on Thursday, with Liverpool having agreed to pay his 19.8 million pound release fee.
The former Partizan player, who turned 20 in March, has been tipped to become a future star, with caretaker Serbia boss Ljubinko Drulovic believing he can become a "major worldwide player" by joining Rodgers' side.
Liverpool is also looking to bring in defensive cover in the form of Southampton defender Lovren, with Daniel Agger's long-term future unclear and Mamadou Sakho, Martin Skrtel and Kolo Toure having struggled at times last season.
Lovren has already stated his desire to join the Merseysiders and will shun interest from Arsenal and Tottenham to seal his dream move to Anfield, with Liverpool just needing to negotiate a fee with Southampton.
A deal for the Croatia center back would represent the Reds' third signing from its Premier League rival, with Rickie Lambert and Adam Lallana having already joined ahead of the 2014-15 campaign.