Read is the former chief of Wunderman, one of WPP's largest agencies. He helped consolidate Wunderman's global services during his time there, a factor that may have weighed in WPP's decision as industry competition intensifies.
The unidentified source told The Journal that WPP would likely announce the appointment early this week after Read's contract is finalized. The decision would end an extended search for the next leader of the world's biggest marketing services agency, after Sorrell's 33-year tenure ended abruptly.
Pressure from major WPP investors and clients to make the company's services more transparent and efficient will also fall in Read's hands, if the appointment is made official.
A WPP spokesperson declined to comment on behalf of WPP, telling CNBC in an email that "There has been a lot of media speculation that we are close to announcing an appointment of a new CEO but until an agreement is reached we will not be commenting."
Read did not immediately respond to CNBC's request for comment.
Previous reports pointed to Read as Sorrell's probable successor after he took on the firm's day-to-day operations when Sorrell resigned.
In June, Sorrell told guests of an event during the Cannes Lions International Festival of Creativity in France that "the plan was for Mark Read and [co-COO] Andrew Scott to be joint chief executives," adding that his abrupt departure was like "being hit by the bus."
Analyst and former media banker Lorna Tilbian, fondly known as the "queen of media," predicted in an April interview with CNBC that Sorrell's departure would lead to a breakup of WPP, which employs over 200,000 employees in 400 separate ad businesses in 112 countries.