Axel Springer is considering an insolvency filing if Kirch does not settle a £470m($667.3m/EUR763.6m) bill by the end of next month.
If such a suit is accepted by the court, a judge could start insolvency proceedings against Kirch.
Axel Springer, the publishing company and owner of the Das Bild tabloid, has an option requiring Kirch to buy back its 11.8 percent stake in broadcaster ProSiebenSat1, which is controlled by Kirch.
The news comes as Kirch today meets its largest lending banks to negotiate the partial break-up of the group.
Kirch Group, the financially-troubled German media company, could be forced into bankruptcy by one its creditors Axel Springer.
