Paul Joakim Sandøy, leader of Norway's Young Conservatives, argues that the pin would represent a "protest against human rights violations and support those who feel that their love is forbidden" .
The call comes after a gay campaign group within the opposition Labour party has called on Solberg to boycott the games in protest at Russia's new anti-gay laws.
According to the Young Conservatives, this would be a "cowardly solution."
"The gay movement, both in Norway and abroad, says that the worst thing you can do is not to go," Sandøy told NRK.
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As well as wearing the pin, the Young Conservatives want Solberg to meet human rights activists and Russian government figures to express Norway's concern at the worsening rights situation for gay Russians.
Solberg told NRK that would not decide whether to wear the pin until she had met gay activists and heard their advice.