The former American Idol contestant is currently the subject of intense media attention after she was spotted embracing married country star Jason Aldean.
She has now been offered her own show by Wag TV, TMZ reports.
The company, which has links to networks such as TLC and A&E, reportedly hoped to make a show following Kerr's attempts to begin a music career.
However, sources have said that Kerr is unlikely to accept the offer.
The singer has previously apologised for her behaviour with Aldean, describing the incident as a "lapse in judgement".