The four aid workers were kidnapped on Friday when militants ambushed a Norwegian Refugee Council convoy and killed a Kenyan driver, officials said.
The Norwegian group has not identified the nationalities of the kidnapped workers.
But a security official familiar with the case said that two of them are from Canada, one from the Philippines and one from Norway. One of the Canadian passport holders is of Pakistani origin, the security official said.
A spokesman for Foreign Affairs in Ottawa declined to comment on the report, saying Canada's top priority was "the safety and security of its citizens."
"We are pursuing all appropriate channels to seek further information and are in close contact with Kenyan authorities," Jean-Bruno Villeneuve said in an email to The Canadian Press.
"We will not comment or release any information which may compromise these efforts.''
A military commander, Philip Ndolo, said that a security escort had originally been arranged to accompany a high-ranking delegation from the Norwegian Refugee Council, but that the aid group decided at the last minute to travel through the Dadaab refugee camp without an armed escort.
Norwegian Refugee Council Secretary General Elisabeth Rasmusson was present during the attack but was not harmed or taken.
Rasmusson said Friday that the attack happened on a main road toward the city of Dadaab in "what is recognized as the safe part of the camp."
She said four men with pistols carried out the attack against the two vehicles. The attackers only took one of the vehicles.
After an attack on a Doctors Without Borders convoy last year in which two Spanish women were abducted, some aid groups began using security escorts in Dadaab, a series of sprawling camps connected by sandy roads. But the Norwegian Refugee Council did not have guards on Friday.
"They had arranged the previous day (Thursday) with the understanding they would get some security officers in the morning, but for some reason they decided not to take the security officers," Ndolo said.
A Norwegian Refugee Council spokesman in Norway, Rolf Vestvik, said a risk analysis was carried out before Friday's movements through Dadaab and it was decided that it was safe for the convoy to travel.
"We wouldn't have carried out such travel if it wasn't seen as being safe," he said.
"But in a situation like that there is always a risk factor and we do everything we can to minimize the risk to our staff. But if you are going to operate in areas where there are refugees you are operating in areas where there is certain risk."
Ndolo said that security officials are pursuing the attackers in an area with no mobile phone coverage, so he is waiting for an update. But, he said, it's possible the group has crossed the border.
"The vehicle was abandoned not so many kilometres from the border, so there is the possibility that if they decided to walk, with an eight hours' walk they would have been at the border, and if they made a connection with other militias they could have been picked up in a vehicle there. That is our worry," he said.
Militants have penetrated Dadaab several times over the last year.
Last October gunmen kidnapped the two Spanish women from Doctors Without Borders. The two are still being held, most likely in Somalia. Several roadside bombs, most of which targeted police, have also exploded in the camp over the last year.
A spate of cross-border attacks last year, including around the resort town of Lamu, is the reason Kenya gave publicly for its military push into Somalia last October to target Islamist militants from the group al-Shabab.
— With files from The Canadian Press