A combination of the two companies would create a business with assets under management or advice of £56bn.
Smith and Williamson is, according to FTAdviser's sister paper the Financial Times, the eighth largest accountancy firm in the UK, and also has a wealth management division.
According to reports, the deal will be structured as a takeover of Smith and Williamson by Rathbones, with the former valued at £600m.
Rathbones has a market capitalisation of £1.4bn.
Rathbones issued a statement this morning (21 August) which confirmed talks were underway, and that the negotiations have been taking place for some time, but there is no certainty a transaction will happen.
The company's shares are up less than one per cent since the market opened this morning. It's stock has risen more than 52 per cent in the past year.
Smith and Williamson is a partnership largely owned by its staff, with the Canadian investment group AGF also a shareholder.
If the deal goes ahead, it will be the latest consolidation in the wealth management industry, and follows in the wake of Canaccord Genuity announcing the purchase of Hargreave Hale last month.
In its most recent set of results, Rathbones announced a 22.7 per cent increase in half-year profits for the period to 30 June, compared with the same period last year.
Smith and Williamson reported a 22 per cent rise in operating profits to 17.7m for the six months to 31 October 2016.