The company could name Taylor CEO as early as Thursday, pending a board meeting Tuesday, according to the report. He currently services as president of Procter & Gamble's global beauty, grooming and health-care division.
Lafley will remain as chairman to help with the transition, the paper reported. He has held the CEO position in two separate periods—once from 2000 to 2009 and most recently since 2013.
P&G—the world's largest maker of household products—has recently been hit by a stronger dollar's effect on sales abroad. Earlier this month it agreed to sell some of its beauty brands to Coty in a deal valued at about $12.5 billion.
P&G reports quarterly earnings Thursday. Its shares have fallen about 12 percent this year.
The company did not immediately respond to CNBC's request to comment.