The Reds will pay a fee that could reach £10 million 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 £25 million. Both moves are being funded by the pending sale of striker Luis Suarez to Barcelona for £75m.
Origi was part of the Belgium squad that reached the World Cup quarter-finals, scoring their winning goal against Russia. There are conflicting reports that Origi would be loaned back to Lille for the season as part of the deal.
Markovic helped Benfica win the Portuguese title and reach the Europa League final last summer after moving from Partizan Belgrade in the summer of 2013.
The Reds, who will return to the Champions League next season, are also keen to sign Southampton defender Dejan Lovren, but have had an initial bid of £20 million rejected.
It has been a busy summer at Anfield already as Liverpool have already signed striker Rickie Lambert and midfielder Adam Lallana from Southampton for a combined fee of £29 million as well as Germany Under-21 midfielder Emre Can from Bayer Leverkusen for £10 million.