Lord Ashdown has accused the government of failing to put pressure on Saudi Arabia and other Gulf states which he said were funding jihadism.
The ex-Lib Dem leader said cutting off jihadists' income should be a "crucial part" of the UK's strategy.
He claimed the Tories' "closeness" to Gulf interests was hampering this.
But he said his party may vote for RAF air strikes in Syria if they were lawful, enjoyed regional support and were part of a broader plan.
David Cameron will make the case for military intervention to MPs on Thursday, stating why he believes extending the UK's existing air campaign against Islamist militants from Iraq to Syria is necessary.
The statement is a prelude to a vote on whether to authorise military action in Syria expected as early as next week.
Mr Cameron has said he will not call the vote until he is certain he can win, having failed to gain the support of Parliament in 2013 for military action against the regime of President Bashar al-Assad.
Lord Ashdown told BBC Radio 4's Today his party - which has eight MPs - had not ruled out backing intervention if key conditions were met and it was a question of what the prime minister "turns up with" on Thursday.
Regional Sunni power Saudi Arabia is part of US-led military action against IS targets in Syria.
Riyadh also agreed to a US request to provide a base to train moderate Syrian rebel forces. The kingdom has been a key supporter of the rebels, including hardline Islamist groups, but it has rejected an Iranian accusation that it has directly supported IS. However, wealthy Saudis have sent donations to the group and some 2,500 Saudi men have travelled to Syria to fight.
The Saudi authorities are concerned that IS will inspire Saudi jihadists to challenge the monarchy's legitimacy and seek to overthrow it.
In July 2014, Riyadh deployed 30,000 troops to beef up security along its border with Iraq, and the following month hosted Iran's deputy foreign minister as the two regional rivals agreed to co-operate.
Asked if the party could support Mr Cameron, he replied "possibly", adding that this was dependent on three factors.
"The first is a clear statement of legality - we have got that from the UN Security Council resolution. The second is a wider coalition spanning the Sunni and Shia divide - that is now being assembled at last and not before time.
"The third is a broader strategy which includes what happens afterwards."
If the international community was serious about tackling violent militant groups such as Islamic State - also known as Isil or Daesh - he said the Gulf states had to play a much larger role in exerting diplomatic and financial pressure as well as military co-operation.
"Pressure on the Gulf states to stop funding Sunni Jihadism and pressure on the Gulf states - if we're going to send our aircraft in, to make sure theirs are present too - is a crucial part of the strategy.
"Will the prime minister ensure now ensure that in the strategy he presents on Thursday, that is part of the strategy?"
And he suggested the government's reluctance to launch an inquiry into the funding of jihadism in the UK was potentially politically motivated.
"The failure to put pressure on the Gulf States - and especially Saudi Arabia and Qatar - first of all to stop funding the Salafists and Wahabists, and secondly to play a larger part in this campaign... leads me to worry about the closeness between the Conservative Party and rich Arab, Gulf individuals.
"Will he launch an inquiry into the funding of jihadism? If not, I think we're entitled to ask some questions about why not."
David Cameron has said the UK must use every resource at its disposal to degrade and destroy Islamic State, which he has described as an "evil death cult". The government is briefing Conservative MPs and members of opposition parties inclined to support the government about its plans.
Yet some senior figures are yet to be persuaded that air strikes will be effective in driving militants out of their strongholds and reoccupying the territory they hold without "boots on the ground" and question who will supply these troops.
Former Labour leader Ed Miliband said he remained to be "convinced" of the case for bombing.
"ISIL have got to be defeated," he told the BBC's Newsnight.
"But who is going to do the ground operations against ISIL in Syria, because there hasn't been a clear answer from the government about that. Secondly, what is the political settlement that we're working towards in Syria, and they haven't been clear about that.
"The PM has promised answers on this, lets see whether the answers are convincing."