Palace see Oosterwolde as a replacement for new Manchester City signing Marc Guehi.
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The Sun says Palace have stepped up their interest in the Dutchman this week, but won't get a clear run at his signing.
Nottingham Forest and Leeds United are also eyeing Oosterwolde this month.
The defender, formerly of Parma, has fully recovered from an ACL injury suffered last season to establish himself as a standout performer for Fener this term.