The Holland international has struggled for minutes at Liverpool, having arrived in the summer from Bayern Munich.
Fotomac says Galatasaray are showing interest in Gravenberch, 21.
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The midfielder is singled out as one of the names at the top of Gala's wish list - as they search for a potential midfield partner for Lucas Torreira.
Galatasaray wanted to sign Gravenberch already last summer - but then he eventually chose Liverpool instead.