Brooks Macdonald approached 7IM controlling shareholder Caledonia Investments about a takeover deal at the end of last year, according to reports.
The £17.3bn asset manager had its offer, which valued 7IM at £300m, rejected by Caledonia.
According to Sky News' sources, the firm is stalking 7IM and is expected to express its continued interest over the course of the coming months.
7IM manages just over £20bn in assets and recently bought two firms - TCAM Asset Management and Partners Wealth Management.
The firm is also dealing with the fallout of two inherited TCAM funds, now 7IM Absolute Return Portfolio and 7IM Income Portfolio, which were exposed to a collapsed securitised debt vehicle.
Neither Brooks Macdonald or Caledonia have responded to requests for comment so far. The deal proposal has not been disclosed to markets.
Caledonia acquired 7IM in 2015, in a deal worth £100m.
Both firms are of a similar size, and their combined £37bn or so in assets would still place them behind some of the larger players in the industry.
The news comes amid a busy period for M&A in the asset management sector, with AssetCo recently striking a deal to buy River and Mercantile Group for £98.8m in an all-share transaction.