Mitroglou was taken to Craven Cottage in January for £12million, but saw injury restrict him to just three appearances.
He was drafted in to aid a survival bid, but a lack of outings contributed to Fulham tumbling out of the Premier League.
It was expected that a man who graced the World Cup finals this summer would be among those offloaded as part of a cost-cutting exercise, with Turkish side Besiktas said to be keen.
Fulham, though, have yet to sanction a sale and Stafylidis, who has moved to west London on a season-long loan from Bayer Leverkusen, would like to see a familiar face stick around and lead a promotion push.
He said: “Of course (I hope he stays). He’s a great guy and speaks my language.
“I think last year he had a problem with injury and hopefully he can come back better and help our team.
“For me he is a good player and I think if he works hard then he is one of the best strikers in Greece.
“I think it’s been difficult for him coming to England and I think this year he will try more and I hope he will help our team.”