Liverpool will pay a fee that could reach up to £10m for 19-year-old Origi, who is set to discuss terms this week.
And they are hoping to conclude a deal for 20-year-old Markovic, who it is understood will cost about £25m.
Both moves are taking place as Liverpool prepare to sell striker Luis Suarez, 27, to Barcelona for £75m.
Barca have indicated they are willing to meet the Uruguayan’s buyout clause but talks continue about how the deal will be structured.
Liverpool are also waiting to hear from the Spanish club’s winger Alexis Sanchez, a target for Arsenal and Juventus.
Manager Brendan Rodgers has not yet given up hope of signing the 25-year-old Chilean but is still awaiting a response from him.
The Reds, who will return to the Champions League next season, are also keen to sign Southampton defender Dejan Lovren, but have had a £20m bid rejected.
Origi was part of the Belgium squad that reached the World Cup quarter-finals, scoring their winning goal against Russia.
Markovic helped Benfica win the Portuguese title last summer after moving from Partizan Belgrade in the summer of 2013.
Liverpool have already signed striker Rickie Lambert, 32, and midfielder Adam Lallana, 26, from Southampton for a combined fee of £29m.
Germany Under-21 midfielder Emre Can, 20, has also moved to Anfield, joining from Bayer Leverkusen in a deal worth £10m.
Written by Steve Milne
