A passenger in front of an American Airlines jet. AP

American Airlines says it will fly its senior executives on the Boeing 737 Max before passengers to show the aircraft is safe.

The plane is grounded worldwide but is due to return to the skies once US regulators approve a software upgrade.

A recent poll found that 41% of Americans said they would not consider flying on the plane until it had been back in service for six months - an obvious problem for airlines trying to sell seats.

Southwest and United Airlines are offering free flight changes to passengers who object to flying on a 737 Max.

American Airlines plans to fly its senior executives on the Boeing 737 Max aircraft before any regular passengers in an attempt to reassure the public that the aircraft is safe.

Doug Parker, the CEO of American Airlines Group, told investors at the company's annual shareholders meeting on Wednesday that executives and staff would take test flights on the plane once the US Federal Aviation Administration approved it to fly again, Bloomberg reported.

The plane has been grounded worldwide since an Ethiopian Airlines 737 Max 8 crashed in March, killing 157 people, five months after 189 people were killed in a crash of a 737 Max 8 operated by the Indonesian carrier Lion Air.

Read more: Nearly half of Americans in poll say they won't fly on Boeing's embattled 737 Max plane until it safely returns to service for at least 6 months

Boeing has completed a software update to the plane intended to address a system that misfired in both crashed jets. Airlines are waiting for FAA approval to put the planes back in service.

An investigator with the US National Transportation and Safety Board at the crash site of Ethiopian Airlines Flight ET 302 on March 12 in Bishoftu, Ethiopia. Jemal Countess/Getty Images

But in the US, many people have seemed reluctant to trust the plane even after it is cleared to fly.

A poll by the investment bank UBS in early June found that 41% of Americans said they wouldn't consider flying on a 737 Max until it had been back in service for six months.

In the meantime, airlines are losing money from not using their 737 Max jets and are eager to find ways to make full use of them when they can.

Read more: Southwest Airlines is going to allow people who don't want to fly on the Boeing 737 Max to switch planes free

Southwest's chief marketing officer, Ryan Green, said in May that passengers who didn't want to fly in a 737 Max would be able to change flights free.

"If they're uneasy about flying on a Max aircraft, we'll be flexible with them," Green told CNBC.

American Airlines Boeing 737 Max jets at a facility in Tulsa, Oklahoma. Reuters

United Airlines also said it would offer free rebookings for passengers who didn't want to fly on the Max planes.

The European Aviation Safety Agency, Europe's aviation regulator, said it had its own requirements for certifying the plane to return, which could mean the aircraft might fly again in the US before it returns in Europe.

Boeing says that the plane design is safe and that it is working closely with regulators. It has repeatedly pledged that when the plane returns it will be one of the safest "ever to fly."

Boeing CEO Dennis Muilenburg said Boeing would "earn and re-earn" the public's trust.

REUTERS/Beawiharta/File Phot

He also said he would be on one of the first flights after the plane's return, calling it a "really important part of showing our confidence" in the Max.

Read more: The FAA says Boeing's troubled 737 Max may not fly again until December - far later than many expected

There is no set date for the 737 Max to return. An official with the US air regulator, the Federal Aviation Administration, said this week that the plane would most likely be back by December.

Ali Bahrami, the FAA's associate administrator for aviation safety, said in Germany that the FAA was under a "lot of pressure" and that the plane would return to the skies "when we believe it is safe."

Parker on Wednesday said it was "highly likely" that the plane would be flying again by mid-August, Reuters reported.

American Airlines CEO Doug Parker. Alex Wong/Getty

American Airlines has canceled flights that relied on the 737 Max - about 115 a day - until September 3.

Airlines are asking for compensation from Boeing over the grounded jets, though most have continued to express confidence in Boeing and in the 737 Max planes.

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