Schroders is also reportedly considering selling a 19.9pc stake in Cazenove Capital, its high-net-worth wealth manager, to Lloyds.
The combined deal was reported to be worth about £500m, with Lloyds’ wealth unit and the Cazenove stake both valued at roughly £250m each.
A spokesman for Schroders said the companies were in talks “with a view to working closely together in parts of the wealth sector”.
They added: “Discussions are ongoing and there can be no certainty that [they] will lead to any formal arrangement being entered into.”
Expanding Lloyds’s wealth management credentials has been a key aim for António Horta Osório, who took charge of the banking group in 2011.