Greece's football association has named Kostas Tsanas as interim coach of the national team, but has yet to confirm predecessor Claudio Ranieri's exit.
The delay in announcing his departure is believed to be because of discussions over a compensation deal.
Former Chelsea boss Ranieri, 63, has presided over three defeats and a draw in Euro 2016 qualifying.
The Group F victory for the Faroes was their first competitive win since 2011 and only their 20th since 1988.
According to local media reports, Hellenic Football Federation (EPO) president Giorgos Sarris and Ranieri met on Saturday and agreed the Italian would leave after Tuesday's friendly at home to Serbia.
But it appears he will leave before the country's next game, with 47-year-old Tsanas to step up from his role as youth coach to take charge of the senior team.
A statement from the Greek FA read: "The Hellenic Football Federation announces that the role of interim coach for the friendly match with Serbia will be (carried out by) Kostas Tsanas and Nektarios Pantazis."
Ranieri managed Chelsea between 2000 and 2004 and was in charge for one season under the ownership of Russian billionaire Roman Abramovich before being replaced by Jose Mourinho.
He has since managed at Valencia, Parma, Juventus, Roma, Inter Milan and Monaco prior to taking the Greece job.
Following Friday's defeat by the Faroe Islands, Sarris said: "I take full responsibility for the most unfortunate choice of coach, which has resulted in such a poor image of the national team being put before the fans.
"The governing board will convene and take responsibility among all the members to make the necessary changes needed to avoid a repeat of such an embarrassing night."
Greece won the European Championship as recently as 2004, beating hosts Portugal 1-0 in the final in Lisbon.