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.
Nemanja Matic enjoying the pressure of playing for 'special' Manchester United
The Russian billionaire has demanded a meeting, to address the lack of academy players deemed good enough for the first team. Sir Alex Ferguson's side of 2006/07 came closest, recording a 8-1 aggregate scoreline over their first two games.
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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