The highly-rated 19-year-old, who has won two senior caps for Greece, is in line for a move to the Stadium of Light.
Panathinaikos are understood to have agreed a deal in principle and now the winger will hold talks with the Black Cats ahead of a possible switch to the North East.
Greek sources claim that Sunderland will pay 4million euros for Mavrias, who has three years left on his current deal.
Meanwhile, reports in France claim Le Havre defender Benjamin Mendy was on Wearside on Wednesday for talks with the club.
The highly-rated 18-year-old full-back has already shunned approaches from Juventus and Inter Milan, but Sunderland appear hopeful of fending off interesting from Lyon to land Mendy.