Mr Corbyn told the BBC Labour would consider the question "as a party".
Ministers have been talking to Labour MPs to try to persuade them to back intervention ahead of a Commons vote expected by Christmas.
Mr Corbyn is against military action, but a number of his MPs support it and may rebel if ordered to vote against.
On his first visit to Wales as party leader, Mr Corbyn said the priority should be a political settlement in the war-torn country, in order to "isolate" so-called Islamic State.
Asked whether he would allow his MPs a free vote - which means they would not have to follow the chosen party line - he said: "No, we would have to consider it as a party, consider it as a group and decide how we would react at that point, I can't predict at this stage."
Events in Syria are "beyond appalling" he said, adding that "there has to be a political solution - all wars end with a political solution".
Prime Minister David Cameron has dismissed suggestions a UN resolution - which Labour is calling for - would be needed before the UK takes action in Syria.
MPs rejected air strikes on Syria in 2013, when the target was President Bashar al-Assad's government in Syria, but later approved British participation in air strikes against Islamic State extremists in Iraq.
The BBC has been told ministers are increasingly confident they will have the numbers to secure Commons backing to extend the campaign into Syria.
Mr Cameron has said he will set out a detailed case for intervention and Defence Secretary Michael Fallon is planning to brief Labour MPs collectively at an open meeting.
Some Labour MPs have already said they will refuse to vote with Mr Corbyn if ordered to oppose air strikes.
Labour leader Jeremy Corbyn has said he will not allow his MPs a free vote on whether to extend UK air strikes into Syria.