Lord Ashdown said Sir Menzies, the deputy leader and foreign affairs spokesman, was the right person to take the party into its next phase.
Sir Menzies is so far the only MP who has said he will stand.
Home affairs spokesman Mark Oaten will say on Tuesday whether he intends to stand. Party president Simon Hughes will announce his plans within a week.
Timetable
The party's federal executive will meet to draw up a timetable to elect the new leader on Monday.
Under proposals to be discussed at the meeting, the new leader would be in place by the end of March.
Nominations would open immediately and close in early February. The ballot papers would be sent to members in late February with voting in March, with the Lib Dem spring conference turning into a hustings event.
Mr Kennedy resigned on Saturday, days after admitting he had a drink problem.
His resignation came after 25 MPs said they would refuse to serve under him.
'Man of substance'
Sir Menzies has the backing of more than a third of Lib Dem MPs, including Lord Ashdown.
He told BBC Radio 4's Today programme: "At the next election he'll offer the British public an alternative that provides weight and substance and seriousness in a political debate that is, frankly, increasingly obsessed with modishness and flim-flam."
Some have suggested Sir Menzies, 64, is too old but Lord Ashdown argued his talents far outweighed other factors.
And he said that although a leadership election would probably be good for the party, people should not be "forced" to stand.
Coronation?
Some backers of Sir Menzies, hope the party can unite around one candidate in a "coronation" - similar to the one in which Michael Howard became Conservative leader in 2003.
But Mr Kennedy and other senior figures say party members should be given a genuine choice amid fears of an acrimonious splits between MPs and the grass roots.
Mr Kennedy said a contest was needed so members could have "direct input" after feeling "shut out" of his departure as leader.
He warned the Lib Dems had to avoid the infighting seen among Conservatives after John Major replaced Margaret Thatcher after she lost the support of MPs despite being popular among party members.
"The danger is there when something like this can happen to a leader who has broad support," he told the Press and Journal newspaper.
Contenders calls
Mr Oaten said he had received many positive e-mails and was "toying" with the idea of contesting the leadership.
He said there should be a contest of some kind as members were feeling "pretty excluded from the process so far".
Health spokesman Steve Webb is urging the Mr Hughes to challenge Sir Menzies and declare his candidacy this week so there can be a debate about the party's direction.
Lib Dem frontbencher Lembit Opik said Mr Oaten was a "very effective alternative" to Sir Menzies and hoped challengers would come forward.
He told BBC News: "It's in nobody's interest to have a single candidate election... We shouldn't be frightened of democracy."
A member of the party's federal executive, Peter Black, said ordinary members felt disenfranchised by the way Mr Kennedy had been toppled.
They could continue to be disenchanted if there was no leadership contest, he said.