That's according to Al Jazeera.
Greece also plans to upgrade 82 F-16s to Block-70 and acquire 24 fourth-generation Rafale fighters from France.
A U.S. congressional committee has also cleared Greece to buy up to 40 fifth-generation F-35 multirole jets.
According to sources that spoke to Al Jazeera, Greece's preferred formula for transferring the F-16 jets is to sell them back to the U.S., which would upgrade them and pass them on to Kyiv.
Some military experts are squeamish about giving away dozens of fighter jets, saying the security concerns that make Greek policy pro-Ukrainian also restrain it.
"The sale of 32 F-16s … would open a big hole in the air force. … There has to be a quorum of about 200 aircraft, which can’t happen with more modern and expensive fighter jets," an air force engineer told Al Jazeera on the condition of anonymity.
Officially, Greece has supplied Ukraine with an additional 20,000 155mm artillery shells, Stinger missiles and 40 Soviet-era BMP-1 armored personnel carriers. It is currently preparing to send four massive transformers that convert high-voltage DC current produced by power stations to the lower AC voltage used on local distribution grids that supply households.
Greece's northern port of Alexandroupolis has a direct rail link with Odesa via Romania or via Lviv. Military equipment can reach Ukraine within 24 hours of offloading in Alexandroupolis.