German side confirm rejected bid for Sunderland winger
Mavrias made 14 appearances for German second division side Fortuna in the second half of last season after joining them on loan in January.
There was a £400,000 clause to convert the loan into a permanent switch, but that has now expired.
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Hide AdHowever, Fortuna have seen a subsequent bid rejected by Sunderland and are now contemplating whether to up their offer for Mavrias, who has just 12 months remaining on his Black Cats contract.
"Sunderland have rejected our offer, which was probably too low," Fortuna head coach Friedhelm Funkel told the German press.
"We have to think about it and I do not know how we will proceed.
"It is quite clear that there are economic limits and we are always looking for alternatives. Whether it works with Mavrias or not, I don't know."
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Hide Ad"Harry is very fast and can play attractive football. I think he is a really good player."
Mavrias - a £2.5million signing from Greek side Panathinaikos in the summer of 2013 - has made just one first-team appearance for Sunderland in the last two-and-a-half years.
That came as a second half substitute in January's FA Cup third round defeat at Arsenal, three weeks before he left to join Fortuna.