Newspaper Klassekampen asked 16 county leaders to vote for the games. 11 gave a 'yes', four were undecided and one said 'no'.
The majority of Conservative Party county leaders said 'yes' to the games, while the Progress Party remains undecided.
The 'no' vote came from county leader, Jo Inge Hesjevik of Finnmark. He is opposed to another Olympics coming to Norway - not just for Oslo.
But Norwegian politicians are overall still more positive to hosting the Winter Olympics then the rest of the population. Polls show most Norwegians are against the games coming to Oslo.
This autumn the government must decide whether or not to back the Winter Games coming to Norway's capital.Their decision will include how much money the government should commit to. This information must be included in Oslo's detailed bid to the International Olympic Committee.
On Monday Oslo was picked out by the IOC as one of three candidate cities to host the 2022 games.