Asked for his views in Bangkok this week, where he attended the International Monetary Fund annual meetings, Healey said the government would study responses to a public consultation that recently closed.
"I think in recent decades, and this is true in Heathrow and airports right across the UK, that they have been a big part of jobs and growth. And the case for a third runway at Heathrow has always been a case for growth," he said.
Healey insisted economic growth was his and Burnham's "number one mission" in government. His predecessor as chancellor, Rachel Reeves, put approval of the runway at the heart of her growth speech last year, saying it would "make Britain the world's best-connected place to do business".
Burnham, who became prime minister in July, has ducked the issue, suggesting it should be "a matter for London and Londoners". The Sunday Times has reported that he told Transport Secretary Heidi Alexander he was "unconvinced" by arguments for the project.
Heathrow's chief executive, Thomas Woldbye, has warned that investors could reassess their backing for the £33bn infrastructure project without the Prime Minister's support. "Our shareholders would like to do this," he said earlier this week. "They do think that things are taking a long time, and so far they have decided to be OK with that ... But of course we cannot wait for ever."
The airport's owners include Qatar's investment authority, French private equity firm Ardian, Saudi Arabia's Public Investment Fund and Singapore's sovereign wealth fund GIC. They are expected to decide in the coming months whether to apply for formal planning permission.
Healey voted in favour of the third runway when the House of Commons last considered it in 2018. He has returned to London to put the finishing touches to his 28 October budget. The IMF praised the UK this week for acting to cut its deficit, with managing director Kristalina Georgieva urging Healey to "stay the course". Official figures on Thursday showed the UK economy unexpectedly grew by 0.1% in August.