The city, which agreed in principle to bid for the Games two weeks ago, plans to hold a non-binding referendum on the issue on when the country goes to the polls in a legislative election.
With less than three months to go until then, 48.4 percent of residents in the capital said they would vote against the idea of hosting the Games, 42.8 percent would vote in favour and the remainder were undecided, the poll showed.
The Sentio survey was conducted June 11 to 16 and questioned 800 people.
Barcelona and Munich have already expressed interest in hosting the Games, as has Krakow, whom Poland and Slovakia plan to link up with in a joint bid.
Stockholm is considering a bid.
Organisers of the Norwegian bid have yet to obtain state guarantees totalling some 33.7 billion kroner ($5.67 billion). The government is expected to provide an answer at the end of the year.
The International Olympic Committee is to announce the host city for the 2022 Games in August 2015.