Sir Menzies was the early front-runner for the post but now the bookies have Chris Huhne as odds-on to win the contest when the results are announced tomorrow (Thursday).
The two candidates, along with Simon Hughes, faced their final and largest official hustings last Thursday, addressing an audience of more than 1,000 people in London.
But, despite Mr Huhne now heading the pack, Sir Menzies remains in confident mood.
He said: "I'm optimistic although not complacent but we have had a tremendously good campaign.
"I have the support of over half the parliamentary party and almost all the Scottish MPs."
While the grass roots support hasn't been quite as favourable, Sir Menzies is delighted with the backing received locally.
He said: "The feedback in the constituency has been tremendous with support from people from all parties, which has been very encouraging," he told the East Fife Mail.
He also insisted that, if he were to succeed as leader, he wouldn't neglect his duties to north east Fife.
"It's important not to lose sight of the fact that MPs are only MPs because of their constituents," he said.
"If I emerge as leader of the party there will still be a commitment to the people of north east Fife.
"I don't think it would make a great deal of difference to the constituency if I was elected.
"It might mean north east Fife getting a little more attention during a General Election but it wouldn't make a material difference."
Sir Menzies was the first to put his hat in the ring for the party's leadership contest, following Charles Kennedy's dramatic resignation in January after admitting an alcohol problem.
During the hustings Sir Menzies (64) told the audience he would be an experienced, credible and campaigning leader and said the party should move from ''mere survival'' to political power.
He also hit back at sniping by his rivals over his position on the Iraq war as the party's foreign affairs spokesman.
He dismissed calls by Mr Hughes and Mr Huhne for the Government to set a deadline under which British forces would be pulled out of Iraq by the end of this year.
Instead, he believes targets should be set for a phased withdrawal.
The three candidates have travelled around the UK facing audiences in areas including Edinburgh, Cardiff and Manchester during an arduous campaign. Britain's 73,000 Liberal Democrat Party members will vote by postal ballot.