The Greek giants have endured a disappointing campaign by their own high standards, even if they are only six points adrift of the leaders in the top flight.
Carlos Corberan, now at West Bromwich Albion, lasted just 11 matches in charge, while his replacement Michel recently announced his resignation.
That has led to Jose Anigo being handed the temporary reins at the Karaiskakis Stadium, but there is every expectation that a permanent head coach will be appointed in due course.
According to Sport-fm, Gerrard is one of the names that is being considered for the lead role in the dugout for 2023-24.
The Englishman has endured a mixed managerial career thus far, winning the 2020-21 Scottish Premiership campaign with Rangers but going on to struggle in his time at Aston Villa.
Gerrard won just 13 of his 40 matches in charge of the Premier League outfit, losing 19 times, and it led to his exit in October.
Since then, his replacement Unai Emery has put Villa into contention for the top six, progression which has not enhanced Gerrard's stock while he has been out of work.
Nevertheless, the report claims that Gerrard is being considered by Olympiacos, albeit only if they fail to attract their primary option.
Gennaro Gattuso, who was sacked by Valencia in January after just 22 games, is said to be the man favoured by Olympiacos officials.
The former AC Milan midfielder is no stranger to Greek football having spent a 17-match spell with OFI during 2014, and it appears that Olympiacos are ready to offer him a chance to return to the country.
Before his short stint at the Mestalla, Gattuso had spells with AC Milan and Napoli between 2017 and 2021, roles which will keep him relevant as a manager despite his recent failure in Spain.