Olympiacos and Standard Liege are in talks with Liverpool over the transfer of Lazar Markovic, Sky sources understand.
The Serbia international has not featured in a competitive game for the Reds since a late substitute appearance against QPR in May 2015 - five months before Klopp replaced Brendan Rodgers as manager.
Since then the 24-year-old, a £20m signing from Benfica by Rodgers in the summer of 2014, has had loan spells at Fenerbahce, Sporting Lisbon, Hull and Anderlecht.
Markovic is currently with the first-team squad for their International Champions Cup campaign in the United States but has played only a minor role in pre-season.
The 22-cap international, who missed out on a place in Serbia's World Cup squad, latched on to a Daniel Sturridge through ball to fire home a stunning opener in Liverpool's 2-0 friendly win at Blackburn last week.