If he wins the next general election Tony Blair would stand down within two years of polling day, the Tories claim.
Mr Blair last week surprised many by announcing he would serve a full term if re-elected, and then quit.
David Davis said Mr Blair had "already fired the starting pistol" on the race to succeed him and his "hunch" was that he would not serve a full term.
The shadow home secretary hinted the Tories would use the slogan "Vote Blair, Get Brown" at the election.
Research showed many Labour voters thought the party was further to the right than it actually was, Mr Davis told a fringe meeting at the Conservatives' annual conference in Bournemouth.
And Mr Brown was seen as an "old-fashioned socialist" by many voters, which is why the Tories had come up with that line of attack.
Mr Davis also warned voters of the dangers of opting for UKIP, saying it would be a wasted vote.
He compared the rise of UKIP to Sir James Goldsmith's Referendum Party, which took "30 to 50 seats away from us" at the 1997 election.
This meant that the pro-European Labour Party ended up with "very little opposition" in parliament, Mr Davis said.
He said the electorate had moved to the right on many issues - such as crime and asylum - but the challenge the party faced was to capitalise on this.
"We have the get the country to buy its conservatism from the Conservative Party," he told the meeting.