The firm is weighing contingency plans, including naming veteran executives Mark Read and Andrew Scott as co-CEOs, the newspaper reported, citing anonymous sources and publication Campaign U.K.
CNBC last week confirmed Sorrell is under investigation after an allegation of "personal misconduct." WPP did not immediately respond to CNBC's updated request for comment on Friday.
The company said last week it had appointed an independent counsel to investigate Sorrell and that the ongoing investigation doesn't appear to be material to the business.
The company expects to complete its investigation as soon as next week, the Journal reported on Friday, coinciding with a previously scheduled board meeting.
Read the full WSJ report here.
—CNBC's Michelle Castillo and Anita Balakrishnan contributed to this report.