Greek winger Charis Mavrias is expected to be leaving the club this summer but the Black Cats will not allow him to move on the cheap.
With a year left on his current contract, the 22-year-old cannot go on a free transfer and was thought to have a £400,000 release fee in is deal.
He spent the last six months of last season at Fortuna Dusseldorf in the German second division and they are very keen to take him back on a permanent basis but their offer has been knocked back by Sunderland as too derisory.
Their head coach Friedhelm Funkel says his club is now weighing up whether or not to lodge an improved bid.
“Sunderland have rejected our offer, which was probably too low,” Funkel told the Chronicle.
“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.”