The meeting between the two Cabinet ministers was being arranged last night as it was confirmed that Mr Rifkind will announce in a separate development on Monday that Britain will not go ahead with its pounds 3bn nuclear Tactical Air to Surface Missile (TASM) programme.
The move means that the RAF will lose its nuclear capability, possibly in favour of cheaper sub-strategic missiles located on Trident submarines.
With Mr Clarke strongly committed to a tough line, Mr Rifkind is said to be squaring up for what could prove a full-scale Cabinet confrontation, which is likely to leave the final decision in the hands of the Prime Minister.
As Mr Clarke met advisers, officials and Treasury ministers to thrash out his budget strategy, there were unmistakable signs that Tory MPs and the defence establishment were mobilising to protect the armed forces from cuts of up to pounds 1bn that the Treasury has been demanding.
The Commons Defence Select Committee will produce two reports on Monday - coinciding with the start of a two-day defence debate - saying that the armed forces are already overstretched. One is expected to argue strongly against further reductions of the Royal Navy's Atlantic Fleet of destroyers and frigates - believed to be a target of Treasury hawks.
The TASM announcement - disclosed in the Independent on Thursday - affects the long-term replacement of the free-fall bomb currently in operation and will generate few, if any, savings in the 1994- 95 financial year, which is at issue in the current spending round.
But it may help to fuel a possible revolt by backbenchers opposed to further defence cuts. Sir Nicholas Bonsor, chairman of the defence select committee, warned more cuts could 'cripple' the armed services.
'If we were to cut further in any significant way then we would undermine our capacity to look after the defence interests of the country,' he told BBC 1's Breakfast News.
Sir Geoffrey Johnson-Smith, chairman of the Tory backbench defence committee, said some of his colleagues would look 'very anxiously' at any further defence cuts.
He told the BBC Radio 4 Today programme: 'We have already committed ourselves to reducing our armed forces by some 20 per cent, including some pretty damaging cuts.'
Sir Geoffrey, MP for Wealden, said ministers should instead look at the Territorial Army and seek cuts that did not harm the integrity of the armed forces. The Treasury is understood to be critical of the number of civil servants at the Ministry of Defence, particularly at senior level.
But David Shaw, Tory MP for Dover, said on the same programme: 'I hope the Chancellor has looked at every single budget from top to bottom.' He agreed that defence 'has to be put on a more realistic basis'.
Kenneth Baker, the former Tory party chairman, urged Mr Clarke to cut interest rates by a full percentage point and phase out mortgage interest tax relief rather than raise other taxes.