The 53-year-old actor has approached the 'Born to Die' hitmaker's representatives about the possibility of her performing, reported Contactmusic.
"Amal is a massive fan of Lana's, which has made George determined to make this happen. He contacted Lana's people to see if she'll perform at their wedding in Italy," a source said.
The 28-year-old singer recently performed at the extravagant nuptials of Kim Kardashian and Kanye West.