The Baltimore-based money manager has been without a permanent leader since former chairman and CEO Mark R. Fetting stepped down on Oct. 1.
The company hired Korn/Ferry International to aid in the search for a CEO.
The Journal, quoting a "person familiar with the matter," said interim CEO Joseph A. Sullivan, who has worked off and on with Legg for the past 19 years, will continue with Legg but in a different role.
Mary Athridge, Legg Mason's spokeswoman, declined to comment on the Journal report
Legg has struggled in recent years to stanch the outflow of money from its funds. The company announced Monday that its assets under management reached $654.1 billion at the end of January, about a third-less than the company managed six years ago.