The grounding of 737 Max airplanes has cost Emirates' sister airline FlyDubai a "lot of profitability" and Airbus planes could now replace some Boeing orders, the Middle East airline's CEO and chairman said Monday.

Ahmed bin Saeed Al Maktoum said Flydubai, a regional partner of Emirates, has had to stop using 40 aircraft due to the worldwide grounding of the 737 Max aircraft following two deadly crashes involving the model. The CEO added that with more than 100 Max 8 planes currently on order, he couldn't "sit and do nothing" and needed to look at options such as the Airbus A320.

"I have to look into a similar type of aircraft, let's say with the Airbus," Al Maktoum told CNBC's Dan Murphy at the Arabian Travel Market trade show in Dubai on Monday.

The Emirates and FlyDubai chief said he would "always demand that we be compensated," but would not yet take the step of officially canceling orders.

When asked how the Boeing crashes could affect the aerospace sector, Al Maktoum said he expected a lot of pressure on the U.S. Federal Aviation Authority (FAA) to be more candid about how it certifies Boeing aircraft.