However, it could be a bad political move for the Liberal Democrats to bolster a party and prime minister who were so comprehensively rejected by the voters, a fear which lay behind Clegg's indication on Friday that he would talk to the Conservatives first.
On Saturday Clegg outlined what his priorities for an agreement with the Conservatives were. He said: "I'm very keen the Liberal Democrats should enter into discussions with other parties as we are doing in a constructive spirit. That's precisely what we will do in the coming hours and days."
Clegg named four main priorities in talk -- schools, tax reform, economic policy and "fundamental political reform to our political system".
Electoral reform, which is a key demand of the Liberal Democrats, is strongly opposed by Cameron and most of his Conservative party.