Everton made Jordan Pickford the third-most expensive goalkeeper in history when snapping him up from Sunderland this summer, but that is not stopping reports linking them with Woodman.
Toffees boss Ronald Koeman is looking to move out Joel Robles to make room for Woodman, but Magpies counterpart Rafa Benitez is not interested in striking a deal.
The England youth international may be behind Rob Elliot and Karl Darlow in the pecking order at St James' Park, but Benitez clearly wants to keep hold.
"The idea is to protect us as a club and make sure he progresses, to keep him until January and then he can go on loan," Benitez has been quoted as saying.
"He can play with the under-23s and stay with the first team and work with the first team 'keepers every day. Then we are covered if we have any problems because he has the quality (to play in the first team).
"Personally he thinks he would like to play because he wants the experience. I told him he can play with the under-23s and we don't want to lose. We have decided that he will stay with us and can go on loan in January if he needs more experience."