The Games kicked off with the opening ceremony last Friday which Debbie Harry says the band was offered a chance to play at.
But the singer said the band turned down the offer due to Russia's stance on gay rights.
She published a picture of a document showing Blondie's official Olympics offer with the words "Pass human rights" scrawled across it on her Twitter page.
Harry also encouraged fans to share the picture to raise awareness, writing: "Pass 4 (for) human rights Sochi 2014 ... Share if you agree ..."
The Sochi Games have been marred by controversy over Russia's anti-gay propaganda laws, which prohibit promoting homosexuality to young people. Pop superstar Cher previously turned down an offer to perform at the Olympics over the legislation.
Instead, the Opening Ceremony featured a performance by reunited Russian pop duo t.A.T.u.
