It said the announcement was being put out in response to press speculation about a deal.
The deal, which would bring together two firms employing about 3,000 people, would see Smith and Williamson hand shares in the combined group to its employees who own the majority of the company, Sky said.
Ryan Hughes, head of fund selection at AJ Bell, said the potential merger between Rathbones and S&W "is the latest evidence that we are in a period of consolidation in the asset management industry".
A Rathbones statement said: "Rathbones confirms that it is now in exclusive discussions with the Smith & Williamson group of companies regarding a possible all share merger of the two groups".
Shares in Rathbone were up 1.2% at 2,803.00 pence Monday. These would be complementary to Rathbones' private office, while both firm's asset management arms would be merged to create a significant player.
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Trump was referring to events in Charlottesville during protests surrounding a decision to remove a statue of Confederate Gen. Lee. "But you know, how many statues of black people are there in the South? He's one of the finest people I serve with".
Sky News first reported on Rathbones' merger plot over the weekend, stating a deal was expected to be announced within weeks and would be in the form of a structured takeover. S&W has been on the block for much of this year after one of its key backers, the Canadian investor AGF, began talks to sell its 30% stake.
Rathbones' swoop on S&W will follow moves by rivals such as Brewin Dolphin to broaden their offering to clients and comes in the wake of stellar growth at companies including Hargreaves Lansdown.
Rathbone Brother Plc is a FTSE 250 company listed on the London Stock Exchange.
S&W, which is being advised on the talks by Evercore, and Rathbones both declined to comment.