“If this continues or gets worse… we will get to the point where we'll have to talk — and Denmark won't be able to do it alone — about adjusting the rules of the game,” Lars Lokke Rasmussen told TV2 television.
The Danish premier, whose Venstre party rules with the backing of the anti-immigration Danish People's Party (DPP) in parliament, said the 1951 treaty should be revised in order to clarify the rights of refugees in the first country they fled to.
“If someone seeking shelter from war has lived for two or three years in Turkey, should he then go to Europe and seek asylum there? As they stand today, the rules allow people to do that, but we are going to have a discussion about that,” he told the Danish television channel.
The prime minister believes the European Union, of which Denmark is a member, should lead an effort to modify the convention, which came into law just six years after World War II ended.
The Danish government's policies on migrants have triggered global controversy, most recently with a plan to seize migrants' valuables and cash.
The plan, which parliament will vote on in January, sparked comparisons to Nazi Germany's seizing of gold and valuables from Jews and others during World War II.
From January to November, 18,000 people requested refugee status in tiny Denmark, which is home to some six million people.
Meanwhile neighbouring Sweden expects the number of requests for 2015 to climb to nearly 190,000.
According to the UN, Turkey is hosting more than two million Syrian refugees.