Origi was pictured arriving in Liverpool on Wednesday to discuss terms with Reds officials at their Melwood training ground and could undergo his medical alongside Markovic on Thursday.
He looks sets to cost Liverpool £10m from French outfit Lille, although Tottenham are attempted to snatch the Belgian striker for themselves.
Origi impressed at the World Cup, scoring for Belgium against Russia during the group stages after replacing Chelsea forward Romelu Lukaku in the starting line-up.
Origi would not commit on where his future lay when asked in an event in his hometown of Houthalen-Helchteren.
“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.”