Senior party figures, including Treasury spokesman, Malcolm Bruce, have warned Mr Ashdown privately of deep alarm in party ranks at the prospect of any form of coalition.
But other leading Liberal Democrats, including Menzies Campbell, Lord Holme and Lord Steel are sympathetic to the idea of taking government jobs.
Mr Blair's allies refuse to rule out the possibility of a Cabinet job for the Liberal Democrat leader. One Labour source described the development as "possible". No detailed discussions between the two men are thought to have taken place.
But suggestions that Mr Ashdown might be brought in have caused reverberations among Liberal Democrat ranks. One senior source said: "I think the motive is a kind of insurance policy. Those of us who are identifiably anti-Conservative would see this as an opportunity to keep the Tories out for 20 years."
Mr Bruce said last week: "I think constructive opposition, as we have established it, is working and I believe we should maintain our freedom to work very constructively with the Government while being completely free to campaign hard and effectively on those areas of public policy where we disagree with the Government and show where they are falling down on their commitments."
Both factions will watch closely Mr Ashdown's next big speech on party strategy, due to be delivered to the Liberal Democrat Spring Conference in March.
Sources close to the party leader acknowledge that Mr Ashdown could not enter into the Cabinet without consultation with the party membership, either through a special conference or a ballot of members.
However sceptics, who include Alan Beith, deputy leader, and Don Foster as well as several new MPs, argue that this may offer little protection against such a move. Under these circumstances Mr Ashdown would negotiate a deal then appeal for endorsement to party members; "it would be back me or sack me".
Mr Beith and other sceptics believe that the only circumstances in which Cabinet jobs become possible would be if Mr Blair were to endorse proportional representation for the House of Commons, and propose a new, beefed-up, joint package of constitutional reform as a platform for a coalition.
But those keen on taking a greater role in government point out that progress has been made on electoral reform and that it is only with ministerial position that real influence can be exerted.
Even they concede that there are only a limited number of Cabinet jobs that would be acceptable or possible following a reshuffle. Mr Ashdown would like to be Foreign Secretary but it is highly unlikely that he would be offered such a senior post with an established incumbent.
Posts in departments such as social security, health or education - where the Liberal Democrats have attacked the Government - are also not feasible. That leaves defence or transport as the most likely post-reshuffle possibilities. Other jobs, including those at minister of state level, could go to Mr Campbell or Lord Holme.Reuse content