Kompany is widely tipped to depart Anderlecht and an announcement is expected to be made today.
Burnley are in talks to appoint the former Manchester City defender as their new manager and the Belgian has not been put off by their relegation from the Premier League.
But there is talk of Kompany having more than one offer on his table and he could still be on his way to Germany after losing out on the Wolfsburg job.
According to German daily Bild, Gladbach are looking at the 36-year-old as a Plan B if they do not land their top target.
The Bundesliga club are in talks with Lucien Favre and they have been expected to get their man this summer.
However, negotiations between the two sides have stalled and French club Nice are in the mix for Favre as well.
Gladbach still want the experienced Swiss coach as their new manager but are considering other options.
And the German club are now monitoring Kompany as a legitimate Plan B if they fail to land Favre.
It remains to be seen whether Kompany can resist an offer to manage in the Bundesliga if Gladbach make an offer to him.
