Boeing CEO Dennis Muilenburg believes the safe return of its best-selling plane, the 737 Max, is the company's most important objective. Boeing is scrambling to restore confidence in the 737 Max from regulators, customers and the flying public. The manufacturer's 737 Max has been grounded across the globe since mid-March after a deadly crash involving the jet in Ethiopia. Less than five months earlier, a Boeing Max crashed in Indonesia. The disasters killed a total of 346 people. Investigators said the jet's MCAS flight control system, which is designed to push the aircraft's nose down to prevent stalling, was involved in the crashes.

Boeing Chief Executive Dennis Muilenburg speaks during a press conference after the annual shareholders meeting at the Field Museum on April 29, 2019 in Chicago, Illinois. Jim Young | Getty Images

"This is a different show for us, it is not about orders. It is really focused on safety and the safe return of the Max flight," Muilenburg told CNBC's Phil LeBeau at the Paris Airshow on Monday. "We are making good, steady progress on the certification work," Muilenburg said, before adding the company was hoping to schedule the certification flight "very soon." The Wall Street Journal reported Sunday that Boeing could start flight testing the Max as early as this week, citing unnamed sources familiar with the matter. Responding to this report on Monday, Muilenberg told CNBC the certification flight would take place in the "near-term" but he refused to provide a more specific timeline.

Safety first