Simon Hughes and Tim Farron are the only candidates for the Lib Dem deputy leadership ballot to be held next week.
Nominations closed earlier on Wednesday in the contest to succeed Vince Cable as Lib Dem deputy leader.
Mr Cable has quit to concentrate on his new role as business secretary in the coalition government.
Mr Hughes is said to have the backing of as many as 29 Lib Dem MPs - making him the firm favourite.
Mr Farron told BBC News he currently has the backing of at least 12 MPs.
The election will be held on Wednesday, 9 June at a meeting of the party's 57 MPs.
Mr Hughes, 57, has been MP for Southwark and Bermondsey for 27 years and is a former Lib Dem president who stood for the party leadership in 2006.
His bid has the backing of Mr Cable - deputy leader since 2006 - and his campaign team say they have been given pledges of support from 29 Lib Dem MPs.
Westmorland and Lonsdsale MP Mr Farron, 40, was first elected in 2005 and is backed by former Lib Dem leader Sir Menzies Campbell, for whom he worked as parliamentary private secretary.
His supporters say he has the backing of at least 12 MPs.
Both have pledged to maintain the Lib Dems' independence - after the party agreed to go into coalition with the Conservatives when the UK general election resulted in a hung parliament.
BBC political correspondent Mike Sergeant said both support the controversial idea of Liberal Democrats having "shadow" ministers for departments where they are not represented in government, arguing that this will allow the party to develop policies and retain its distinctive identity.
But there will be concerns that these "shadow" ministers become the focus of opposition within the Liberal Democrats to coalition plans.
One of Nick Clegg's advisers said the deputy prime minister had "no plans" to appoint Lib Dem "frontbenchers" in areas where they're not represented in government.
He said the leadership was discussing with MPs how the party operates within the framework of the coalition and that the views of the deputy leadership candidates would be considered as part of that debate.