The companies are believed to be in the final stages of talks and hope to announce the deal in the next week or two.
Quilter, which has almost £8bn under management and can trace its heritage back to 1771, will take the bulk of the top board positions under the deal.
Its chief executive Martin Baines has been lined up to run the new firm, while Cheviot’s chairman Sir George Mathewson is set to leave the enlarged company following the merger.
Bridgepoint acquired Quilter in February, pledging at the time to seek out bolt-on acquisitions.
The private equity firm is putting up the funding for the purchase of Cheviot, which has around £4bn in assets under management.
Baines told City A.M. the firms “had long looked at each other with mutual respect”, and that the new company would have a “critical mass in London and a strong regional presence”.