Sky Sports sources on Friday reported a delegation from St James' Park had travelled to Holland to hold talks regarding the Dutchman.
Newcastle are understood to have failed in an initial £8million bid for De Jong earlier in June and Twente boss McClaren remains unwilling to sell.
The former Middlesbrough and Nottingham Forest manager is quoted as telling Dutch media: "Luuk de Jong would stay if it were up to me - unless stupid money is offered.
"The club know what I think about it."
It has in the past been reported Twente value De Jong at closer to at least £12.5million so it remains to be seen whether Newcastle are prepared to meet that asking price.
Magpies boss Alan Pardew had in January shown interest in the 21-year-old, who was an unused member of Holland's disappointing Euro 2012 squad, but he 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.
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