Burnham and other potential candidates have from 9 July to 15 July to collect the backing of 81 MPs, and until 16 July to gather the required number of nominations from affiliated bodies such as trade unions, to stay in the contest.
While on a visit to Anglesey, Stevens said she was “very sad” about Sir Keir Starmer’s resignation, describing him as an “absolutely brilliant prime minister”.
She said: “He’s taken the party from oblivion in 2019 through to the biggest general election win in my lifetime and delivered across the United Kingdom over the past two years.
“So, I’m very sad to see him go.”
Asked if she would like to continue as Secretary of State for Wales, Stevens said it was “an enormous privilege to serve in government”.
“It will be up to Andy Burnham, if he’s the new prime minister, to decide who he wants in his cabinet, and we’ll wait and see what happens”.
Stevens was appointed as Welsh Secretary in July 2024.