"I'm supporting Andy to be prime minister," she told the BBC on Thursday after Burnham emerged as the only declared candidate to replace Keir Starmer, who announced his resignation on Monday.
Starmer said he would oversee an orderly transition after bowing to pressure over weak poll ratings and poor local election results, triggering a leadership contest set to begin on July 9.
Reeves, a close ally of Starmer, said no one could doubt her commitment to the outgoing prime minister, adding that she had worked alongside him for six years.
Burnham, who is the only candidate to have put his name forward, is widely expected to be installed without a challenge, meaning he could become prime minister by mid-July.
If appointed, he would be Britain's seventh leader in a decade.
Asked about reports she could be demoted, Reeves said cabinet decisions would be a matter for Burnham.
"I'm not going to pre-empt the decisions that the new prime minister will make. I'm backing Andy. I think he'd be a great prime minister, but those are his decisions, not mine," she said.
She said she stood ready to provide targeted, temporary support on energy bills later in 2026.
Reeves said the next leader should stick to her fiscal rules, including balancing day-to-day spending with tax revenues and reducing debt as a share of output.
Burnham has previously signalled he would keep current borrowing rules in place.
"I know that whoever is prime minister and chancellor in the future will inherit a stronger economy than the one I inherited two years ago," she said.
