The 35 year-old departed the Greek Super League giant after both parties agreed to terminate his contract just three months into his second spell at the club.
West Ham was among the Premier League clubs linked with the midfielder when he left Manchester City at the end of last season, and speculation has suggested he is ready to head back to England.
Writing on his official Facebook page, Toure thanked the Olympiacos fans for their support and made it clear his passion for the game has not waned.
"To the Olympiacos fans. I came back for you. I had a vision and wanted to win trophies for you," Toure posted on Wednesday.
"Sadly, it has not worked out. But I move on with love in my heart for you all. You have always encouraged me and stood by me.
"But now it is time for a new challenge. My love for football still burns strong."
Toure made just five appearances in his second spell with Olympiacos, with some reports in Greece suggesting he had failed to convince manager Pedro Martins of his worth to the team.
However, it has also been claimed his 'pay as you play' deal was becoming problematic for the club due to budget restrictions.