The club is emerging as a potential replacement for Alexander Isak, who has been linked with a departure.
Woltemade has attracted interest from Bayern Munich, but VfB Stuttgart's valuation proved a hurdle.
Newcastle is now in contact with the German club and is prepared to offer £65 million for Woltemade before the upcoming deadline.
VfB Stuttgart has informed Newcastle that they are willing to do business, with the offer consisting of an initial £60.5 million plus £4.5 million in potential add-ons.
Both parties appear confident that Woltemade will join Newcastle in the coming days.
