The Brazilian, 24, has scored eleven goals and 15 assists in 38 Feyenoord matches this season.
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He has been linked with Liverpool, but is now a priority target for Napoli.
Il Mattino says Napoli see Paixao as a replacement for Khvicha Kvaratskhelia, who was sold to PSG in January.
AC Milan and Inter are also interested in Paixão - who has a contract until the summer of 2029.