Wealth manager Tilney made a move for Smith & Williamson after it emerged the firm was in £2bn merger talks with Rathbone Brothers.
The wealth management rivals confirmed earlier this month that they had entered exclusive discussions over a tie-up.
After news of the discussions emerged, Tilney, which is majority-owned by private equity firm Permira, is understood to have approached Smith & Williamson.
Sky News first reported that Tilney had made an all-cash offer for its rival but that Smith & Williamson expressed a desire to pursue a Rathbones merger deal instead.
Tilney, Smith & Williamson and Rathbones declined to comment.
News of competing offers for Smith & Williamson comes at a time when more mergers and acquisitions (M&A) are expected in the asset management industry, which is facing regulatory changes and the rise of passive managers.
Aberdeen Asset Management and Standard Life completed their tie-up this month, while Henderson Group and Janus Capital also recently merged.
Read more: Analysts expect more asset management M&A