Rathbones said the two companies were in exclusive discussions with Smith & Williamson over an all-share merger, as first reported by the Sunday Times.
"However, if agreed, any such transaction will be subject to the approval of shareholders".
Sky reports that Canadian firm AGF, which owns 30% of Smith & Williamson, has been looking for an exit for some time.
Le geste d'un nageur aux victimes des attentats de Barcelone (vidéo)
Ce que je ressentais était plus fort que si j'avais gagné toutes les médailles d'or au monde. Fernando Alvarez devait disputer le 200m brasse à Budapest, lors des World Masters Swimming.
The alliance will attribute a valuation of close to £600m to S&W, a market source said this weekend, and will involve issuing Rathbones shares to its target's investors. The paper said the combined company would have more than 3,000 staff across the UK.
Any deal between Rathbones and S&W would also see the unification of their fund arms. The FTSE 250 company has a market value of £1.42 billion and more than £36 billion of assets under management.
Meanwhile, Smith and Williamson's funds business manages a range of diverse products across asset classes, including those focused on Europe, the Far East and the United States, as well as the Global Gold and Resources fund.
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