According to Sky Sport, the Premier League club have submitted a €27 million offer, while Trabzonspor are holding out for €30 million.
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The two clubs are believed to be close to reaching an agreement, with the transfer expected to be completed early next week.
The 22-year-old Nigerian centre-back is set to sign a four-year contract at Craven Cottage once the deal is finalised.
Nwaiwu joined Trabzonspor from Austrian side Wolfsberger AC in January and quickly became a defensive mainstay.
He scored three league goals, provided one assist in 16 appearances, and helped the Black Sea Storm lift the Turkish Cup.