Private equity group Bridgepoint, which bought Quilter from Morgan Stanley earlier this year, will facilitate the merger.
Quilter CEO Martin Baines said: “When Bridgepoint invested in Quilter earlier this year, we stated that an active search for complementary acquisitions would follow.
“We are currently in exclusive discussions with Cheviot Asset Management and expect to be able to provide more information in due course.”
Sky News reported that Bridgepoint is expecting to pay less than £100m to acquire Cheviot, although this has not been confirmed by any of the involved parties.
The merged wealth manager, which Sky suggested could be called Quilter Cheviot, would run about £12bn in client assets and would be the second-biggest independent private client management firm in the City after Brewin Dolphin.