The Sun says United are keeping tabs on the 17 year-old's progress this season.
United had scouts posted last week to see Kostoulas in action against Twente in the Europa League.
The striker is also being tracked by Bayern Munich, Juventus, Fiorentina and Borussia Monchengladbach.
Kostoulas has a deal with Olympiacos to 2026 and is a Greece U21 international.
This season, he has two goals and an assist in 10 league matches.