He also said that the party with the "greatest mandate", even if they have not won a majority, should be given the first chance to form a government.
Labour's Harriet Harman said it showed Mr Clegg was "prepared to back David Cameron and the Tories once again".
Mr Clegg said he was not "expressing a preference" but he wanted "stability".
In other election news:
Polls suggest a hung Parliament is likely after the 7 May general election, leading to speculation on how the next government might be formed. The SNP is also forecast to increase its share of seats.
The deputy prime minister spoke to the BBC following an interview with the Financial Times in which he ruled out helping to establish a government dependent on "life support" from the SNP - which was seen as a blow to any chance of a Labour-Lib Dem coalition after 7 May. He also suggested that any coalition formed by the second largest party would lack "legitimacy".
Mr Clegg told the BBC: "I'm not expressing a preference about who the Liberal Democrats talk to after May 7 - that's for the British people to decide. I'm expressing a strong preference for stability over instability.
"If no-one wins a majority - and they are not going to - on May 7, for me I think it is very important that people understand that Liberal Democrats will ensure that any government is legitimate and stable.
"That means that, in a democracy, the party with the greatest mandate from the British people - even though they haven't got a majority - seems to me, to us, to be the party that has the right to try to assemble a government first. They may not succeed, but they should surely be given a chance to succeed."
Labour has ruled out forming any coalition with the SNP and its leader Nicola Sturgeon has dismissed the prospect of a coalition but has offered to work with Labour on an informal basis to keep the Conservatives out of government.
Main pledges
Policy guide: Where the parties stand
BBC political correspondent Ben Wright said Mr Clegg had not definitively ruled out the possibility of both the Lib Dems and the SNP supporting a Labour government's Queen's Speech.
While Ed Miliband and David Cameron have refused to discuss how their parties would respond to a hung Parliament, Mr Clegg has been happy to discuss hypothetical scenarios, promising his party would ensure a government would not "lurch off to the extremes".
He recently told the BBC he would not agree to another coalition with the Conservatives if they insisted on their planned £12bn welfare cuts.
The Lib Dem leader has also previously ruled out a deal with both the SNP and UKIP.
He told the Financial Times he had no "meeting point" with either party because UKIP wanted to withdraw from the EU and the SNP to "pull our country to bits".
There has been speculation about whether the Lib Dems would agree to an EU referendum as part of any deal with the Conservatives - who have pledged a vote in 2017 - and what they would demand in return for doing so.
Former leader Lord Ashdown, who is running the party's election campaign, said the Lib Dems would not have a "formal deal" with a party that would "break up the United Kingdom, or indeed, with a party that would take our country out of Europe and would plunge us into appalling right wing policies and mountains of cuts".
Asked about Mr Clegg's comments while on the campaign trail in Croydon, Mr Cameron said a Conservative majority was "within our grasp" - and if he could achieve that then all the problems of coalition wrangling would go "out of the window".
"Voting Liberal Democrat is like Forrest Gump - you don't know what you're going to get. They're saying they could be just as likely to support Labour as to support the Conservatives," he added.
On a visit to Stevenage on Saturday, Labour Leader Ed Miliband said:  "I'm concentrating on the issues at this election. That's what I'm going to do for the rest of this campaign because I think there are huge issues on the ballot paper, issues like the National Health Service, issues like the economy we create.
"So, we'll leave it to others to commentate. We are going to go out and fight for what we believe in this election."
Responding to Mr Clegg's comments, UKIP Leader Nigel Farage said: "At the end of the day this isn't about what people think, this is about arithmetic. It depends what happens in this campaign in the next 12 days.
"I feel the UKIP campaign is strong, I feel we're picking up support in our target areas and if we win enough seats, whatever they've said about us they might just want to talk to us."
A YouGov poll of 1,594 adults for The Sun suggested Labour was maintaining a two-point lead on 35% to the Conservatives' 33%, with Ukip on 13%, Liberal Democrats on 8% and Greens on 6%.
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Lib Dem leader Nick Clegg says his party will not prop up any government "held hostage" by the SNP or UKIP, should there be a hung Parliament.