Franklin Resources Inc. is in talks to buy rival asset manager Legg Mason Inc., according to people familiar with the matter, in a deal that could help two big players in an industry that is under pressure from shifting investor tastes.

Assuming it comes together, a deal for Legg Mason could be announced as soon as Tuesday, the people said. While the exact price and other terms couldn’t be learned, it would be sizable given Legg Mason’s market value of more than $3.5 billion and assets under management of $800 billion.

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