Fortounis, 26, has enjoyed a simply stunning campaign in Greece, racking up 17 goals and 16 assists in all competitions for Olympiakos.
The playmaker is unsurprisingly attracting major interest, and West Ham director of football Mario Husillos is keen to land him having seen him first-hand during his time with Olympiakos.
It's now claimed that Olympiakos want at least €17million (£15million) for Fortounis, and the man himself has decided that he'd rather stay and sign a new contract than move on to West Ham.
That's a blow for the Hammers, who appear to be pushing to sign another playmaker to offer some competition for Manuel Lanzini, or even some cover given that he's being linked away.
The former Kaiserslauten attacking midfielder has shown his quality in Greece, possessing great quality on the ball, a decent turn of pace and dangerous set pieces.
At £15million, Fortounis could have been a fine addition to Manuel Pellegrini's side, even if he's only really starred in Greece.
West Ham should pursue a deal for a couple more weeks in an attempt to try and change his mind, but this may well be a major blow for Husillos and Pellegrini.
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