Education Secretary Alan Johnson has said he "fully expects" to vote for Gordon Brown to become the next Labour party leader.
He told BBC One's Sunday AM programme that the chancellor "would be an excellent prime minister".
Mr Johnson revealed last week that he would not contest the party leadership when Tony Blair stands down, but would instead pursue the deputy leadership.
It would be "fine" for Home Secretary John Reid to run for leader, he said.
Mr Reid has not revealed his intentions, but Mr Johnson said of any contest: "Gordon has made it clear himself that he would welcome a challenge.
"I don't think it's a necessity, though."
There was no need to "gerrymander" a contest for its own sake, Mr Johnson added.
Many observers had thought that the education secretary, a strong supporter of Mr Blair, would stand against Mr Brown.
But he said: "I've always been complimentary about Gordon."
Any Cabinet led by Mr Brown had to be a "government of all the talents," he added.
Pensions Secretary John Hutton told Sky's Sunday with Adam Boulton that it was very unlikely he would want to run for leader.
But the contest was an important process that could not be carried out in an "atmosphere of intimidation".
Mr Reid has not "thrown in the towel", according to Westminster sources.
However, Mr Brown's only confirmed challenger is left-winger John McDonnell.
Cabinet ministers Peter Hain and Hilary Benn, Constitutional Affairs Minister Harriet Harman and backbencher Jon Cruddas have already declared their intention to run for the deputy leadership.
Commons leader Jack Straw is also thought likely to enter the race.
The current deputy prime minister, John Prescott, has said he will stand down within the next year, when Mr Blair quits as Labour leader.
Mr Johnson says he has the backing of the 44 Labour MPs needed to stand.
Mr Prescott would not tell BBC One's Politics Show which candidate he was backing as his successor.
But he said that becoming deputy leader did not necessarily mean becoming deputy prime minister, as this was "in the patronage of the prime minister".
Mr Prescott added: "I'm not sure that every candidate has an idea that they just want to be deputy leader.
"They may have an idea that they want to be deputy prime minister."