The 34-year-old signed a one-year contract with the option for a further year when he left Real Madrid last summer after 15 years in the Spanish capital.
Marcelo has made 10 appearances for Olympiacos and scored three goals but has been sidelined recently because of injury.
Reports suggest Marcelo has received an offer from an unnamed club which he is evaluating.
"I have lived unforgettable moments in Greece. Piraeus and its people have all my heart," Marcelo said on social media.
"This won't be my last time in this amazing country. I can only express gratitude for wearing the Olympiakos jersey. Even though the brief stay, the experience and the friends I made there will be forever marked in my life."
"The entire Olympiakos family would like to thank Marcelo," the Greek Super League side posted on social media.
"The time he stayed with us was brief but enough to create everlasting bonds. He knows that in Greece, in Piraeus he will always have friends."
Marcelo left Real Madrid last summer as the club's most decorated player, winning 25 trophies, including five UEFA Champions League titles and six La Liga trophies.
Marcelo won 58 caps for the Brazil national team.
