The chairman of HS2 is facing the sack less than five months after his appointment because of fears that costs are spiralling out of control.

Sir Terry Morgan is also set to be removed as the chairman of Crossrail, the ambitious line linking east and west London, relieving him of leadership of two of the UK’s highest-profile infrastructure projects, according to a report.

The move would represent an embarrassing setback for the transport secretary, Chris Grayling.

Theresa May was expected to move against Morgan, who was described as “world-class” by Grayling when he appointed him in July to HS2, the planned high-speed rail link between London and Birmingham. A source said that Morgan was expected to leave both posts within weeks.

The news was first reported by the Financial Times on Friday. It is thought that both Grayling and the chancellor, Philip Hammond, had declared they had no confidence in Morgan’s leadership and urged May to remove him.

The FT quoted a government official close to HS2 as saying: “They told the prime minister they have no confidence in him and she agrees. It is only a question of finding the right moment to announce it.”

Downing Street, the Department for Transport and HS2 declined to comment. The DfT said: “We would not comment on personnel matters.”

The paper also reported insiders within London’s City Hall as saying Morgan would step down from Crossrail after falling out with the mayor, Sadiq Khan, as costs rose and the hopes of revenue in the short term fell after deadlines for its opening were pushed back.

“The more people looked into what was happening at Crossrail, the more they realised that Terry Morgan wasn’t the person to take a massive project like HS2 over the line,” the FT quoted the government official as saying. “There are a whole load of companies waiting for HS2 to start awarding contracts for the construction phase, but we are still awaiting final decisions. People are kicking their heels.”

Grayling had allied himself closely to Morgan in the summer. “Sir Terry’s appointment as chair of HS2 ensures that we will continue to see world-class leadership in an exciting period for one of Europe’s most significant infrastructure projects, helping deliver huge economic growth and improvements for passengers across the country,” he said when he announced the decision.

Morgan, the transport secretary added, had a “wealth of experience and expertise”, as well as a “respected reputation and enthusiasm”. He cited Morgan’s work on previous infrastructure projects, including upgrading several London Underground lines and working at BAE Systems. Morgan said the appointment was a “privilege” and promised HS2 would “help transform this country”.

But concerns were raised about its direction after it emerged days after Morgan’s appointment at HS2 that Crossrail was running about £600m over budget. And, in August, the government’s infrastructure adviser said ministers should devolve an extra £43bn to local leaders across the country to spend on transport projects to maximise the benefits of HS2.

In an article for the Sunday Telegraph, the chairman of the National Infrastructure Commission, Sir John Armitt, said the government “cannot simply construct a new high-speed rail line and leave it at that; to get the biggest bang for our buck, we need to think about the whole journey that passengers will take”.

He went on: “Once people reach the end of their HS2 journey and travel into the city they are visiting, on current form, they would in many cases face inadequate public transport links and congestion on the roads.” To deal with that, he suggested handing the cash to local areas to improve their infrastructure.

There were further reports that HS2’s budget could eventually spiral to £80bn. The Sunday Times said a leaked report had warned that the official budget of £56bn for the project may have to be significantly increased.

• This article was amended on 6 December 2018 to more accurately describe Armitt’s recommendation of spending a further £43bn on other infrastructure projects.