Speaking on the BBC Radio 4 Today program, Lord Dannatt said the so-call Islamic State of Iraq and the Levant (ISIL) terrorist group had to be "opposed, confronted and defeated" in both Iraq and Syria.
"The Syrian dimension has got to be addressed. You cannot deal with half a problem," he said.
"The old saying my 'enemy's enemy is my friend' has begun to have some resonance" with our relationship with Syria and its allies.
"I think it's going to have to have some resonance with our relationship with Assad."
Dannatt continued: "I think whether it is above the counter or below the counter, a conversation has got to be held with him. Because if there are going to be any question of air strikes over Syrian airspace it has got to be with the Assad regime's approval."
The former army chief said he believed more UK special forces might need to be deployed on the ground in Iraq to train Kurdish troops in how to use weapons. He also suggested the "time will come" when the government decides that British planes should carry out air strikes, rather than leaving it to the US.
Although US officials have described ISIL as an "apocalyptic" organization that poses an "imminent threat", the highest ranking officer in the American military said that in the short term, it was sufficient for the US to "contain" the group, which has taken over large chunks of territory in Syria and Iraq.
The army general Martin Dempsey, chairman of the joint chiefs of staff, said on Thursday that cross-border action was necessary to defeat the group. He played down, however, speculation that US warplanes would strike ISIL in Syria as well as Iraq.
NJF/NJF