The Premier League club have long been linked with the Netherlands international, who went to Euro 2012 but did not play in his nation's disappointing campaign.
Newcastle have now made their first approach and Sky sources understand Twente are considering the offer as boss Steve McClaren thinks about the options.
The pursuit of De Jong will do little to quash reports Demba Ba is set to leave St James' Park this summer and it appears to be the case of Alan Pardew lining up replacements.
It has in the past been reported Twente value De Jong at closer to £12.5m so it remains to be seen whether Newcastle are successful in their initial approach.
Pardew had in January shown interest in the 21-year-old but instead decided to bring in Papiss Cisse from Freiburg.
De Jong has also been linked with Tottenham, Liverpool, Bayern Munich and Borussia Dortmund after scoring 39 goals in 76 games for Twente.