The request was sent to the Australian embassy in Washington yesterday and the federal government is considering it.
NZ Defence Minister Gerry Brownlee said there had been no such request from the US to New Zealand, and one was not expected.
Mr Brownlee said expanding New Zealand's role was not an option at this stage.
Australia is already involved in bombing IS targets in Iraq, but its aerial role in Syria has so far been limited to refuelling and intelligence-gathering.
New Zealand and Australia are both involved in training troops in neighbouring Iraq.