The Conservatives say they have been targeting Lib Dem and Labour MPs in an effort to get them to defect.
Mr Cameron is promoting 'liberal Conservatism'
Shadow chancellor George Osborne said he offered Lib Dem frontbencher David Laws, seen as being on the right of his party, a seat in the shadow cabinet.
But Mr Laws is reported to have told Mr Osborne he is not a Tory.
It came as David Cameron launched a fresh bid to woo Lib Dem voters, saying them there was a "home for them in the modern, moderate Conservative Party".
The Tory leader's move on to traditional Lib Dem territory, such as the environment and social justice, has been seen as an attempt to grab votes in Lib Dem-held marginal seats in the South of England.
Within days of becoming leader in 2005, Mr Cameron launched a website urging Lib Dem supporters to defect.
He will renew his charm offensive later in a speech in Bath, when he will call for Liberal and Conservative supporters to "rally together behind an alternative government-in-waiting".
He will say the time was right for a "new Liberal-Conservative consensus" combining individual freedom and social responsibility.
The divide in British politics today is between a Labour government that seeks "state control" and liberals and Conservatives who want a society based on "social responsibility, Mr Cameron will add.
Lib Dem leader Sir Menzies Campbell sparked speculation he wanted to form a coalition with Labour in the event of a hung parliament, with a speech last month setting out "five tests" for a Gordon Brown-led government.
He said that "of course" the Conservatives were not up to the challenge of meeting these.
But senior Conservatives believe they can exploit differences at the top of the Lib Dems between figures such as Mr Laws, whose belief in a free market agenda was expressed in a book of essays called The Orange Book, and others who wanted to form a coalition with Labour.
Mr Cameron will say: "There is a question mark over the future direction of the Lib Dems, between the Orange Book Liberals and what we might call the Brown Book Liberals - those who look forward to a coalition government with Gordon.
"But there is no question mark over the future direction of the Conservative Party.
"We have a philosophy - liberal Conservatism - which has the answers to the great questions our country faces."
Speaking to GMTV's The Sunday Programme, in an interview to be broadcast this weekend, Mr Osborne confirmed he had held a "private conversation" with Mr Laws, but declined to discuss it in detail.
He added: "We are a big tent. We welcome in people from across the political spectrum. We've got councillors who have switched over to us and there's a real sense at the moment that the excitement is with us, that people are coming to join us.
"We talk to lots of people. I've had conversations with Labour MPs and Liberal Democrats but no-one yet has taken the bait."
Press reports last month suggested that Mr Osborne "invited himself in" to Mr Law's office at the Commons and told him he would be offered a shadow cabinet position if he defected to the Conservatives.