The poll found that 38 per cent would support an alliance with Labour, with 16 per cent favouring a repeat of the deal with the Conservatives.
Almost a quarter said the party should not form another coalition.
The ComRes poll also found that councillors backed Vince Cable as their preferred candidate to replace Nick Clegg if he quit as party leader, with 38 per cent backing the Business Secretary.
Party president Tim Farron was the choice of 27 per cent of councillors, with Treasury chief secretary Danny Alexander the third most popular candidate on 10 per cent.
Some 45 per cent of councillors supported a ban on the wearing of a burka in places such as schools and airports, with 38 per cent opposing such a ban.
The poll, for BBC Sunday Politics, found 86 per cent supported a mansion tax on homes valued at more than £2 million, 72 per cent backed the scrapping of the Trident nuclear deterrent and 70 per cent were in favour of reinstating the 50p top rate of income tax on incomes above £150,000.
A third supported the banning of Page 3 pictures with 46 per cent opposing such a move.
Employment minister Jo Swinson told a Sunday newspaper that a coalition with Labour was not impossible.
“Working in a mature and adult way where you recognise what your shared goal is – that is not something which I think would be particularly more difficult with Labour than it is with the Conservatives,” she said.