Tunstall provides care services and assisted living for elderly and disabled people at home, with devices like alerting systems and monitoring technology.
Any sale is in its early stages and could take place at the end of this year or early next year, the source added, cautioning that no deal was certain.
Charterhouse, Tunstall and JP Morgan declined to comment.
The company had previously set out its new five-year strategy following a 2014 review, as it aims to digitalise the business and provide integrated health and social care, as the technology for so-called “smart homes” gathers pace.
Tunstall plans to invest up to £100m pounds over the next five years as it pursues that strategy, the source added.
The healthcare services sector has proved attractive to private equity and strategic companies alike. BC Partners is currently selling German laboratory operator Synlab in a possible 1.7bn euro deal.
Charterhouse paid £530m for Tunstall in 2008 and has since made several bolt-on acquisitions in Europe and the United States, according to the fund’s website.
The buyout house last week sold its stake in environmental consultancy Environmental Resources Management (ERM) to Canadian pension fund Omers for an enterprise value of $1.7bn.