The Turkish website reports that the 24-year-old Serbian winger is set to depart for Greece on a year-long loan deal for the 2018/19 campaign - in what will be his fifth loan move since joining Liverpool in 2014.
Markovic, who arrived at Anfield with high hopes and a £20m transfer fee, has so far had stints at Fenerbahce, Sporting CP, Hull City and Anderlecht, but failed to excel during any of them.
The Serbian left Benfica for Merseyside in 2015 as one of the hottest prospects in European football but struggled to cope with the demands of Premier League football. After featuring 19 times in the league under Brendan Rodgers in 2014/15, he quickly fell down the pecking order and has not been considered by Jurgen Klopp.
While Markovic was one of 26 players to report for pre-season training with Liverpool earlier this month, there is little chance of him impressing enough to stay with the first team beyond August 9.
Markovic is in the final year of his contract and another loan move this season appears to show that Liverpool have given up on recouping close to the £20m fee they paid for him, prior to his contract expiry next summer.
Markovic will still be hopeful of resurrecting his career in Greece with Olympiacos, who finished third in the Greek Super League and are looking to win their 45th league title in 2019, after AEK Athens ended their run of seven straight league victories last season.
The winger featured for Liverpool in their pre-season friendly defeat against German club Borussia Dortmund on Sunday, but his last competitive outing for Liverpool remains a late cameo in a win over QPR back in May 2015.