Chancellor Gordon Brown is "without doubt the strongest candidate" to become the next prime minister, says the Lord Chancellor, Lord Falconer.
The peer, a close ally of Tony Blair, stopped short of formally backing Mr Brown but said he told GMTV the chancellor was a "towering" figure.
Only one MP - John McDonnell - has said he will challenge Mr Brown but he may not get enough endorsements to run.
Unless another figure comes forward, Mr Brown will take the helm unopposed.
Lord Falconer, who has been one of Mr Blair's most loyal supporters in government, said Mr Brown's achievements put him "head and shoulders" above potential rivals.
"Once he became the prime minister, or leader of the party, of course he would have my backing."
In an interview to be broadcast on GMTV's Sunday programme, Lord Falconer said: "He is the person, along with Tony Blair, who has most contributed to what the Labour Government has done over the last nine-and-a-half years."
Speculation about a challenge from the Blairite wing of the party has centred on home secretary John Reid, one of the few front bench figures still to declare his hand.
'Likely course'
A speech this week by Mr Reid on the future of New Labour was interpreted by some Labour MPs as veiled leadership bid.
But Lord Falconer said "the most likely course" was for Mr Brown to become leader.
He stopped short of backing Mr Brown, but said: "Once he became the prime minister, or leader of the party, of course he would have my backing.
"I don't know what's going to happen between now and the time that he actually takes over, which I think is probably the most likely course."
Lord Falconer, a close friend and former flatmate of Mr Blair's, said he had "no idea" about when Mr Blair would stand down.
Candidates
Mr Blair announced at the Labour Party conference in September that it would be his last has prime minister.
Left-winger John McDonnell is the only person who has publicly declared that they intend to contend the vacancy, which is due to come by next August at the latest.
Anyone who wants to join the contest to succeed Mr Blair has to get the backing of 44 Labour MPs.
The candidates then go forward to a vote, with Labour MPs, Labour members and unions each making up one third of the electorate.
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