Trian reportedly held discussions with the firm encouraging it to cut costs and improve margins, people familiar with the matter told the Journal.
"We would note, Trian has had success with other financial services firm's investments including State Street and they already know Legg Mason and the asset management business," an analyst at Gabelli Securities said in a note Wednesday. " Regardless of the potential Trian involvement, we believe the shares are attractive with positive current variables."
Legg Mason, a Baltimore-based investment firm with $758 billion in assets under management, has struggled lately with its focus on active money management as low-cost passive investing in index funds and exchange-traded funds takes over the financial industry. Shares of Legg Mason have returned a negative 4% a year the last five years, badly trailing the 10% positive return of the overall financial industry and the .
The report did not say whether Trian is building a stake or not in the stock. The deadline for funds to reveal their holdings for the first quarter is Wednesday. Shares of Legg Mason have rebounded by more than 37% this year, including a 2.6% pop Wednesday.
Trian used to be a major shareholder of Legg Mason but after the company's restructuring program, Trian sold its position to the Shanda Group. Peltz left the board in 2014.
"While Trian did not file a 13F yet, we view this positively as it raises our confidence behind LM's $100M+ 2Y expense cut target," Credit Suisse said in an instant reaction for clients.
While the potential activist campaign is being viewed by many as a margin optimization story, Gordon Haskett Research Advisors noted that the financial industry is "ripe for more consolidation."
Legg Mason and Trian both declined to comment to CNBC.
— Read the full story from the Wall Street journal here.
— With reporting by CNBC's Tom Franck.