New Zealand is one of the "Five Eyes" partners - an intelligence sharing alliance with the US, Australia, Canada and Britain.
Little said the reports were yet to be verified but it was a worry if there was any suggestion sensitive security information was given to another state which should not have it.
"But we are part of a security network and all partners to that network must maintain the integrity of that network."
Asked if he would have concerns about sharing with a Trump Administration if he was Prime Minister, Little said he would make a judgment on that if he was Prime Minister after September.
"I think it is important for those security relationships and partnerships to operate is that everybody has to trust each other. In the end, it's a matter for this Government to make a judgment right now about whether that trust is there."
Foreign Minister Gerry Brownlee said the media reports had been rejected by senior US officials at the meeting.
"If there is ever to be a resolution of the dreadful situation in Syria, it will require concerted efforts from both the US and Russia.
"I hope the meeting between President Trump and Foreign Minister Lavrov is a step towards that."
He did not say whether the Government was concerned or had sought reassurances about the handling of its intelligence information.
Prime Minister Bill English is in Japan and could not be contacted for comment.