The Gossip singer was thrilled when the 'Hung Up' hitmaker cited her solo material as an influence on her forthcoming album 'M.D.N.A' and now wants to collaborate further.
She said: "I was over the moon when I heard that [I'd influenced Madonna]. I got a fire in my ass about wanting to write for her.
"I was like, 'Get on the horn and call me, Madge! Does anyone have Madonna's phone number? Oh, hold on, no one does.' "
Part of Gossip's new album was produced by Mark Ronson and Beth says they bonded over hip-hop and country music.
She told NME magazine: "I loved Mark and we worked really well together, he's a really amazing singer's producer. Just the way he gets a voice out of you is so special.
"He has such a vast knowledge of music and had so many great references that we totally shared.
"He really does love music and you can tell. One of our most Common bonds was we both loved big voices, church voices. He loves country music, which is a big deal to me because, in terms of things I love, country music is probably number one, then it's punk and hip-hop.
"With Mark, we both loved a certain type of late to early 90s hip-hop and R&B."