The Brazilian striker is about to enter the final year of his Cottagers contract.
The London Evening Standard says Fulham will consider offers for the former Tottenham centre-forwrd.
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Fulham are comfortable moving on Vinicius with Jay Stansfield impressing on-loan at Birmingham City.
Rodrigo Muniz is viewed as Fulham's No1 striker, with Raul Jimenez his primary backup.