Alan Pardew has been after the Holland international for more than a year.
Twente boss Steve McClaren is thinking about the options.
Reports that Demba Ba is set to leave St James' Park this summer has got reporters saying Pardew is lining up replacements.
But with Leon Best and Peter Løvenkrands leaving the club, Pardew has always said he was in the market for a new striker.
Allegedly Twente value De Jong at closer to £12.5m but the player did did not feature in Euro 2012 so his value has not gone up during the competition, and if anything, may have dropped.