Earlier this month the newspaper had said that the fast-food tycoon was considering making a bid for CKE.
However, after conducting due diligence, Peltz has decided not to enter into a bidding war with private equity firm Thomas H. Lee Partners, which had agreed to buy the restaurant for $619 million in cash, the paper said.
CKE Restaurants and Trian Fund Management could not immediately be reached for comment by Reuters outside regular U.S. business hours.
Shares in CKE closed at $11.25 Wednesday on Nasdaq. (Reporting by Anuradha Ramanathan in Bangalore; Editing by Greg Mahlich)