Pardew reportedly believes that he can sign the former Netherlands Under-21 international in a £5 million deal.
The report has also claimed that Huddersfield manager David Wagner could consider selling Van La Parra for the right offer.
Van La Parra scored two goals and provided three assists in 39 Championship starts for Huddersfield last season.
Both West Brom and Huddersfield are struggling for survival in the Premier League this season.
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