The Switzerland international has already revealed his desire to join the Bundesliga outfit, but the two clubs have not yet agreed a transfer fee. Die Fohlen are allegedly willing to pay €7 million for the 19-year-old, whereas Basel are hoping for a sum closer to €10m.
Gladbach sporting director Max Eberl is said to have begun negotiations last Sunday, with more to come during the next few weeks.
The German club will have a sizeable transfer kitty after confirming the €17.1m sale of Marco Reus to Dortmund, and Xhaka is the club's first choice to replace Schalke-bound midfielder Roman Neustadter. The 19-year-old Basel man's current contract is set to expire in 2015.
Gladbach currently sit fourth in the Bundesliga, and with two games to go, are fighting for an automatic berth in the 2012-13 Champions League group stage.