The 21-year-old has long been linked with a move to the Borussia Park outfit, who are chasing a replacement for Marco Reus following the German's move to Dortmund this summer
Die Fohlen lost star striker Marco Reus to Borussia Dortmund, and have consistently been linked with a move for the Netherlands international throughout the summer.
However, the Enschede outfit were reluctant to sell the 21-year-old, sparking a row with the player, who has maintained that he has his heart set on a move to Borussia Park.
And it seems that De Jong has moved one step closer to his goal by agreeing a five-year contract with Gladbach, but a spokesman has stressed that they have not struck a deal with Twente themselves.
The Dutch outfit were believed to be holding out for a €20 million transfer fee for the striker, but would be willing to accept an offer of €15m.
"We have made sensible and smart transfers," Gladbach vice-president Ranier Bonhof commented. "The depth of our squad is getting better. Every player has quality now."
De Jong, who was also courted by Newcastle this summer, scored 25 goals in 33 Eredivisie games for Twente last season, and has reportedly passed a medical with the Bundesliga club.