The Enschede side insist they are in no rush to sell their most prized asset, but concede that negotiations have begun with the Bundesliga outfit with a view to a possible transfer
The 21-year-old has been consistently linked with a move away from the Dutch outfit after netting 25 times in 33 Eredivisie appearances last season.
A host of Premier League clubs are also said to be interested in his signature, but Twente coach Steve McClaren issued a hands-off warning to potential suitors in an attempt to appease the speculation.
However, the club's negotiator, Aldo van der Laan has now admitted that he has spoken to Gladbach sporting director Max Eberl, although he did stress that an agreement between the two clubs has yet to be reached.
"Max Eberl was here for two hours, but we are far from an agreement," he told RP. "For us, there is no need to sell De Jong.
"We are ready to talk if the fee offered reflects the players quality and the time remaining on his contract. I can say that there are many interested clubs."
Twente president Joop Munsterman has also warned suitors that it would take a sizable offer for him to part with De Jong and denied rumours that a €15 million bid would be enough to allow the striker to move on.
"We don't expect Luuk to leave the club," he told Eredevisie Live. "We will not let go of him for €15m. You have to reconsider when an insane off is made, thought. You can think about €20m then."
In addition to selling Reus to Borussia Dortmund, Gladbach have sold lost Dante to Bayern Munich and Roman Neustadter to Schalke, but have brought in Alvaro Dominguez from Atletico Madrid and Granit Xhaka from Basel.