The CEO of United Airlines is said to have pitched a blockbuster merger with American Airlines during a meeting with Donald Trump, floating the combination of the world’s two largest carriers.

Scott Kirby, who leads United, raised the prospect during an encounter with the US president in late February, Reuters reported, citing two unnamed sources. Such a deal would overhaul the global air travel industry – and likely face intense competition scrutiny.

United declined to comment. American and the White House did not immediately respond to requests for comment.

Including international flights, United and American were already the world’s two biggest airlines by available capacity last year, according to OAG, the aviation data group.

Shares in United rose 3.9% during early trading in New York on Tuesday. Shares in American climbed 9.3%.

A combination between the two carries would be the largest consolidation move in the airline industry in at least a decade, combining the “big four” of the US sector – United, American, Delta and Southwest – which collectively already control 74% of passenger capacity, into the “big three”.

It is unclear how Trump responded to Kirby’s proposal. A merger between United and American would probably face staunch opposition from unions, rival airlines, lawmakers and airports – and spark fears around overlapping routes and job losses.

Critics swiftly warned that any such deal would also have a detrimental impact on passengers.

Ganesh Sitaraman, director of the Vanderbilt Policy Accelerator, and author of Why Flying Is Miserable, said: “A potential United-American merger proves how broken the airline industry is in America – and would be an absolute disaster for the flying public. Fewer choices mean higher ticket prices, more fees, and fewer options for anyone who wants to get from point A to point B. Even the most permissive antitrust regulator should put their foot down at such a blatantly anticompetitive merger.”

But Capt Dennis Tajer, the spokesperson for the Allied Pilots Association, a union representing the 16,000 pilots of American Airlines, approached the report with an open mind.

“We have been very open about our concerns regarding American Airlines’s financial, operational and customer service underperformance under the current management team,” said Tajer. “We are always interested in and welcome ideas that will turn around our airline.”

Sean Duffy has suggested that there is scope for consolidation in the air travel industry, but stressed any deal would face close scrutiny. “If there was a merger between some of the larger airlines, they would have to peel off ​some of their assets,” the US transportation secretary told the CNBC news network last week. “I am not ​going to pre-commit to anything.”

“Who knows who is going to match up?” Duffy added. “Is there room for some mergers in the ​aviation industry? Yeah, I think there is,” he said, acknowledging there had been “​a lot of chatter” about potential deals.

Reuters contributed reporting