The mosque project began in 2007 in the face of strong opposition from the influential Orthodox Church of Greece and nationalist sentiment against neighboring majority-Muslim Turkey.
“Procedures were to a certain extent delayed during the pandemic, but we are speeding up work and aim to have the mosque running by the end of autumn,” the ministry of education and religious affairs said in a statement to AFP.
Another government source said the end of October was a realistic target "barring another lockdown".
Greece was ruled by the Ottoman Empire for centuries, and Athens is the only European capital without an official mosque.
The Athens mosque, which can accommodate some 350 people, was completed with state funding in 2019.
The only officially sanctioned mosques in Greece are in the northern border region with Turkey where some 150,000 members of a Muslim minority live.
Elsewhere in the country, Muslims - many of them refugees and migrants - pray in improvised sites in flats and basements.
There are some 250,000 Muslims in Athens alone, according to estimates.
Earlier this week, the Muslim association of Greece protested against the imminent closure of a prayer hall in the port city of Piraeus that had operated since 1989.
“Muslims (in Greece) are far from reaching equality in law and society,” the association said in a Facebook post.
The Piraeus hall lacked a permit, and will allowed to reopen if it passes evaluation, the government source said Friday.
“All who apply receive a permit, if their papers are in order,” the source said.
The education and religious affairs ministry said it has sanctioned another seven prayer halls in the greater Athens area, including one near Piraeus.