Kenney told CBC's Carol Off that the UN High Commission for Refugees has not formally approached Canada about a Syrian refugee resettlement program, but he said there have been "informal soundings."
"The soundings are about a very small and discrete potential resettlement program for people who have extraordinary high needs for resettlement," Kenney said during an interview on As It Happens. "That might be women who have been abused in refugee camps, things like that."
Kenney said the Canadian government is looking at how it could potentially participate in a "limited program," and that he believed the UN is potentially looking to find places for a few thousand people with a high need to be relocated.
The immigration minister said the scale of the Syrian crisis means it can't be solved through resettlement alone, noting that humanitarian support is also critical to supporting people displaced by the clashes between rebel fighters and forces loyal to President Bashar al-Assad.
The UNHCR says there are more than 1.6 million registered refugees from Syria, with thousands more leaving the war-torn country every day. Many flee to neighbouring countries, including Jordan, Turkey and Lebanon, where humanitarian agencies have been working to keep up with growing demand.
"Canada will participate in a limited way, for people with particularly high resettlement needs. There will be opportunities for private sponsorship of refugees, but let's not delude ourselves into believing we can somehow solve the broader program through resettlement," Baird said.
Prime Minister Stephen Harper announced at the recent G8 summit that Canada is providing $115 million in new funding to address humanitarian needs in Syria and surrounding countries, which have been dealing with an influx of refugees. Kenney pointed to Canada's humanitarian contributions, which have been used to deliver food, water, medicine and other supplies to people displaced by the bloody conflict.
Canada's situation is further complicated by existing commitments to resettle Iraqis who were in Syria. To date, 15,000 primarily Iraqi refugees out of Syria have been resettled in Canada, Kenney said, with more waiting for their applications to be processed.
But the immigration minister did say the country is willing to work with the UN.
"Until now, formally they've told us they're not encouraging resettlement as an option," Kenney said. "We understand that may be changing in the near future, and as I've said we're willing to co-operate with the UN when we hear more formally what they're looking for."
Syrian refugee resettlement was an issue on Parliament Hill this year, with the NDP calling on the government to do more to reunite Canadians with Syrian relatives who have been displaced by the violence.
'Straining at the seams'
Kenney's interview came a day after Adrian Edwards, a chief spokesman for the UNHCR, told CBC that "things are really straining at the seams" as the refugee crisis worsens around Syria.
"That's why we increasingly think it is important that we start to engage with governments around the world on discussions of resettlement," Edwards said Wednesday.
Edwards said the UNHCR is holding discussions with a number of countries about resettlement for displaced Syrians.
"I think it's fair to say at the moment our immediate focus is with European governments, but we're looking at all the countries that are traditional resettlement partners to find some solution," he told CBC's As It Happens on Wednesday.
Edwards said the agency has discussions with Canada every year about resettlement because of the country's history of hosting people driven out of their homes.
"I don't know at this stage whether we're reaching a point of making formal requests, as such, but with all the countries we're talking resettlement with, we're talking about the challenges presented by the Syria situation."
The conflict in the country has grown increasingly violent, with reports of heavy shelling and clashes in recent weeks in Aleppo, Damascus, Dar'a, Homs and other areas. Recent reports indicate the government has used chemical weapons, prompting the U.S. to say it will provide arms to rebel forces seeking to oust Assad.
Edwards said it's "early in the day" to see exactly how the Syria situation will unfold, but noted that it's clear that help is needed for the Syrian refugees.
"Or ultimately, we risk being a society that produces double victims — that is, people who are victims of war on the one hand, and victims of a world that does not want to sufficiently help on the other," Edwards said.