The centre-back has been linked with a move away from the Dutch club for some time, with the Magpies leading the chase for the 24-year-old.
The 2010 Eredivisie winners have settled on life without the towering defender, who only has a year left of his contract, not wanting to risk him leaving for free at the end of the season.
"Both clubs [Fulham & Newcastle] told us they want to do business with us", Munsterman told Voetbal International .
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"We didn't received any offers yet, but when they want to pay a fair price, Douglas may leave the club. Because otherwise he will leave Twente for free next year."
The player had revealed that there were five clubs in the running for his signature, with Newcastle one of the favourites, and admitted he hoped his future would soon be resolved.