"We want to put together a plan that gets maximum value and does the most good for refugees," he told reporters during an event to mark World Refugee Day at Ottawa City Hall.
"We don't have that plan finalized just yet."
The Canadian Immigrant Settlement Sector Alliance has called on Alexander to commit to sponsoring at least 10,000 Syrian refugees by the end of 2016.
No decision yet on Canada's total commitment
In an interview with CBC News Alexander said he welcomed the group's proposal, but said the government has not yet come to a decision on how many Syrian refugees Canada will ultimately take in.
"It's possible to imagine a very large number of government-assisted [Syrian refugees]," he told CBC News.
"We know we'll be able to do much more if we combine our government assistance with innovative forms of private sponsorship … We will have an ambitious goal for Canada, but we need to prepare the ground with our private sponsors."
The federal government has promised to resettle 1,300 refugees by the end of this year, but groups who work with refugees say problems with processing make it unlikely Canada will reach that target.
More government support needed, say sponsor groups
Earlier this week, Martin Mark, the refugee sponsorship coordinator for the Catholic archdiocese in Toronto, told CBC News that, as it stands, private sponsors can’t get the support they need from the federal government.
"They need a very serious change which must include open communication with the society, with stakeholders, with sponsors. Otherwise, there is no way," he said.
Correction : This story has been updated from a previous version that incorrectly stated Alexander had announced $51 million in new money for UNHCR. In fact, it is not new money.(Jun 20, 2014 4:23 PM)