More than 5 million voters will receive the leaflet, which carries pictures of the two Tory heavyweights and statements on Europe from each. It asks bluntly: "Are you more a Clarke Conservative than a Hague Conservative?"
The politically explosive move, by the breakaway Pro-Euro Conservative Party, comes as Mr Hague's position as leader appears increasingly shaky.
Sharp divisions among the shadow cabinet emerged last week following the announcement of plans - on the night of a dinner to celebrate the 20th anniversary of Baroness Thatcher's election as prime minister - to abandon the Tories' free-market approach to the welfare state. She has reportedly "gone ballistic".
Yesterday, John Major came under pressure to abandon his safe Huntingdon seat to Chris Patten, the former governor of Hong Kong, who has been tipped as another candidate to lead the Tories.
The anti-Hague leaflet, which places Mr Clarke at the forefront of a potential leadership bid, is designed to encourage a protest vote against the Tory leader in June's elections to the European Parliament. The authors, two Euro MPs who resigned the Tory whip last year in protest at his decision to rule out British entry into the single currency for the time being, hope that a poor showing in the polls will bring about a leadership challenge. They believe Mr Clarke could help to revive the fortunes of the Conservative Party by staking a claim for the middle ground.
"In a whole range of respects Clarke is a much better leader than Hague," said John Stevens, one of the leaflet's authors. "Our objective is not to turn the Tory party into a pro-European force but into a force capable of winning votes from the public."
Mr Clarke is likely to distance himself from the leaflet but he has not ruled himself out as a potential leadership contender. Last week, it emerged in Donald Macintyre's biography of Peter Mandelson, that Mr Clarke, who is in favour of close co-operation within the EU, held secret meetings with Labour in the last general election to dissuade Mr Blair from taking a more sceptical line than the Tories on the single currency.
Mr Hague's new policy of using tax revenues to fund hospitals and schools also came under attack last week. Senior members of the shadow cabinet, including Ann Widdecombe, the health spokesman, indicated they would ignore it. The policy shift, set out by Peter Lilley, has also sparked divisions in the Tory 1922 Committee.