Southwest Airlines is preparing for the expected return of its grounded Boeing 737 Max 8s as early as this summer and concedes some concerned travelers will initially avoid the plane.”There’s certainly going to be some people that, I expect, will probably book away for some period of time,” Southwest President Tom Nealon said on the airline’s quarterly earnings conference call Thursday.Nealon said there is no way to measure how many concerned travelers will avoid the plane or for how long, but he emphasized that Southwest still expects to fill all the returning planes given strong travel demand and the airline’s loyal customer base.”I don’t think it’s going to be a massive issue for us,” he said.The airline has 34 Max 8s in its fleet, more than any other U.S. carrier, and has had to cancel thousands of flights since the March 13 grounding of the plane following two fatal crashes in five months.More: Boeing 737 Max: How many of the planes fly for Southwest, American and United, and where? Nealon said Southwest has been surveying customers about their perceptions of the plane, awareness and understanding of the issues surrounding the grounding and any concerns they have, as it prepares a campaign to reassure travelers the Max 8 is safe.There is no timetable for the return of the Max but Southwest CEO Gary Kelly said Thursday he expects the grounding to be lifted in the “relatively near future.”He said he expects Southwest’s fleet and operation to be back to normal by the third quarter or beginning of the fourth quarter. The third quarter runs from July through September.Southwest has taken the Max 8 out of its flight schedule through Aug. 5, but has said it will use the Max 8 as spare aircraft if the Federal Aviation Administration lifts the grounding before then.The FAA has to sign off on software fixes Boeing implemented to address anti-stalling system issues that figured into the two crashes, which killed 346 people. Boeing CEO Dennis Muilenburg said Wednesday on the company’s earnings conference call that Boeing has completed 135 Max 8 test flights with the software modifications, and noted that he’s been on two of the flights.The next step is FAA approval for the changes and training plans and the authorization for the planes to fly again. Muilenburg said he expects that in the “near term.”More: Boeing CEO seeks to reassure 737 Max changes will workMike Van de Ven, Southwest’s chief operating officer, said Southwest can have the planes back in service about a month after the grounding is lifted. Southwest’s Max 8s are in storage in California and the airline is using the downtime to get the planes in shape for as quick a return to service as possible.Perhaps the biggest challenge ahead: convincing skittish travelers the plane is safe. The Max grounding has even infrequent flyers asking airlines what plane they will be on. Southwest gets questions daily about the Max 8 on Twitter, with many passengers mistakenly thinking they are on a Max 8 because the airline has the same safety information card for the Boeing 737-800 and the Max 8. Southwest, other Max operators and Boeing are feverishly working behind the scenes to come up with a plan to reassure travelers that the plane is safe to fly when it returns.More: How will airlines convince skittish passengers the 737 Max is safe to fly again?“We know we have some work to do to earn and re-earn the trust of our customers and the flying public in particular,” Muilenburg said on Boeing’s quarterly earnings conference call Wednesday. He said Boeing is “going to make an investment” in this area and suggested airline employees, especially pilots who fly the plane, will be featured in any public relations campaign.American, which has 24 Max 8s in its fleet, has already said its pilots will play a key role in helping convince customers the plane is safe to fly after the grounding is lifted.Southwest didn’t reveal what it plans to say to customers and employees about the return of the Max 8 and its safety but Nealon said the airline will have a “very comprehensive plan.”Kelly said Southwest will definitely share with travelers steps the airline has taken to ensure the plane is ready to return.