The Black Cats are believed to have agreed a £2.5million fee for the 19-year-old Greece international who has two caps to his name.
It would appear to be third time lucky for Di Canio who failed with a move to lure Mavrias to the Stadium of Light last month, whilst hopes of a loan deal fell through last week.
But with the two clubs finally seeing eye to eye, Mavrias is expected to discuss personal terms and undergo a medical within the next 24-48 hours.
Mavrias holds the distinction of being the second youngest player to play in the Champions League - at the age of 16 years eight months - when he was handed his debut for Panathinaikos, playing the final 12 minutes of a goalless draw at home to Rubin Kazan.
Mavrias has since made more than 60 appearances for Panathinaikos, scoring six goals.
Should Sunderland complete the deal, Mavrias will join the other 10 new faces under Di Canio this summer in Ondrej Celustka, El-Hadji Ba, Emanuele Giaccherini, Jozy Altidore, Vito Mannone, Modibo Diakete, David Moberg Karlsson, Valentin Roberge, Cabral and Duncan Watmore.
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