The Sun say United are monitoring the 17-year-old's progress this season.
United had placed scouts last week to watch Kostoulas in action against Twente in the Europa League.
The striker is also followed by Bayern Munich, Juventus, Fiorentina and Borussia Mönchengladbach.
Kostoulas has a contract with Olympiakos until 2026 and is an international for Greece U21.
This season he has two goals and an assist in ten league matches.
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