The Magpies have been tracking the 21-year-old for some time and have already had a €10 million (£8 million) bid rejected but are reported to have increased that to €12m (£10m).
Twente are thought to want €15m (£12.1m) for the Holland international with the Tyneside club having flow a delegation of club officials over to the De Grolsch Veste for talks.
And manager Alan Pardew will certainly be confident of getting his man after De Jong’s agent Louis Laros admitted his client is ready to leave The Tukkers before the new season begins.
“Luuk has taken the decision to move on,” Laros told TC Tubantia. “He wants to develop as a player in a bigger league.
“The important thing for us is the development of Luuk. Not the money, but the way of playing and the amount of playing time he will get will be decisive.
“Luuk scored 25 goals in the Dutch league last season, how many more does he need to score? 35?”
He added in Voetbal International: “Luuk is still a Twente player. If the right club comes along then he will happily make the move.
“The club doesn’t need to be a top club, but a good club in a big league where Luuk can play regularly and develop as a player.”
De Jong scored 25 goals in the Eredivisie last season and has also attracted the attentions of German side Borussia Monchengladbach who were said to have made an offer over the weekend.
Newcastle are also working on deals for Lille defender Mathieu Debuchy and Ajax utility man Vernon Anita as they prepare to embark on their first European campaign in five-years