The 22-year-old Nigeria international has attracted strong interest after an impressive second half of the season following his move from Austrian side Wolfsberger AC in January.
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Nwaiwu scored three goals and provided one assist in 16 league appearances, while also helping Trabzonspor lift the Turkish Cup.
Trabzonspor are understood to have already rejected two bids from Fulham, while Bayer Leverkusen are also monitoring the centre-back.
Turkish outlet Taka Gazete claims West Ham have seen a €30 million offer turned down, with Trabzonspor holding out for at least €35 million before considering the sale of one of their prized defensive assets.