Woodman worked with Alan Pardew at both St James' Park and Charlton Athletic previously, and following George Wood's departure from Palace at the end of last season, the Eagles have been looking to appoint someone.
Woodman's son Freddie completed a loan move to Crawley Town until January on Wednesday, fuelling rumours he will follow him to the south east and take up a position at Selhurst Park.
The Shield Gazette report that Palace and Newcastle are continuing to negotiate a compensation deal after initially failing to agree a package.