"We will switch to the MAX if we cannot resolve our issue. We will go to current option 737s and convert it to MAX," he said, adding he was sure Boeing could find production slots.
Al Baker has refused to accept planes with engines made by Pratt & Whitney, a unit of United Technologies Corp, because the engines required additional time to start under certain conditions.
The airline said in May it was reducing the frequency of more than a dozen regular routes from Doha because of hold-ups in the delivery of new planes from Airbus.
The delays are affecting Qatar Airways' profit, but the carrier is not seeking compensation, Al Baker told reporters on the sidelines of the International Air Transport Association annual meeting in Dublin.
"We are five aircraft down this summer. This is why we are screaming because it is making a huge impact on my bottom line," Al Baker told journalists.
"We are still at an impasse. We have walked away from our first A320neo because it is more than a certain number of days late, so exercised a walk-away clause," Al Baker said, adding the carrier would exercise walk-away clauses on the other four delayed planes when they reach the time limit.
He added he is also still waiting for deliveries of three A350 planes, which have been held up since February due to issues with cabin equipment.
He said he expects Airbus to deliver 10 of the planes as promised this year and that he had met with the CEO of Airbus's planemaking unit, Fabrice Bregier, and programme executive Didier Evrard on Thursday to "iron out the issues".
"The ball is in court of Airbus. We will start delivery of the airplane delayed from February imminently, provided the issues we have are resolved," he said, adding the A350 problems were likely to be resolved before the A320neo issues.
Pratt & Whitney in a statement said Al Baker's remarks were "inaccurate and mischaracterize the performance of the engine."
Pratt's PW1100G-JM engine has been certified, has been delivered to three other airlines and meets performance and contract specifications, including a 16 percent improvement in fuel efficiency, the company said.
"We have resolved the very few initial teething items airlines have experienced," Pratt said. "Production engines shipping today to Airbus already include hardware and software improvements. In fact, solutions for the items are well known and have been extensively covered in detail by the media."