The Benfica winger was pictured at Portea Aeroporto in Portugal on Saturday morning and is understood to be on his way to Merseyside.
Markovic was originally scheduled to fly in on Thursday after the Anfield outfit agreed to pay the €25 million release clause in the player's contract.
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But the transfer is now set to be completed this weekend as Liverpool pushes ahead with summer recruitment plans following the 70 million pound sale of Luis Suarez to Barcelona.
Markovic, who turned 20 in March, was part of an impressive forward line which helped Benfica to a place in the Europa League final last season.
However, he did not play in the penalty shootout defeat to Sevilla after being sent off from the bench in the semifinal against Juventus following an altercation with Mirko Vucinic.
Liverpool is also close to completing deals for Southampton center back Dejan Lovren and Belgium international Divock Origi.
The Merseyside club has already signed Saints pair Adam Lallana and Rickie Lambert, and former Bayer Leverkusen midfielder Emre Can.
Brendan Rodgers is bolstering his squad as the club aims to maintain last season's Premier League title challenge while competing in the Champions League.