The 30-year-old winger was signed by Rafa Benitez in the summer of 2010 on a Bosman transfer, but the Spaniard soon left Anfield and Jovanovic was rarely involved thereafter.
He has made just 10 appearances since his move from Standard Liege and now looks set to depart.
Jovanovic has confirmed that he is looking for a new club and Greek giants Olympiakos are said to be leading the chase.
"I got the paper from Liverpool that I am free to search for a new club," he told the Greek media.
"Up to now, I still haven't received an official offer from Olympiakos, but I am looking forward to hearing their plans."
Jovanovic could also have options back in Belgium with Anderlecht and Club Brugge keen, whilst German clubs Schalke and Stuttgart have also been linked as they tried to sign him before his move to Anfield.
The news that Liverpool have told Jovanovic he can go will come as little surprise as they are actively looking for a new left-winger, with Aston Villa's Stewart Downing seemingly top of their wish list.