The 'Girls Gone Wild' singer is a ''huge fan'' of the teen pop sensation and wants them to hook up at on of her summer concerts.
When asked what she thought of Justin in a live twitter chat with fans, Madonna replied: ''He's awesome. I'm a huge fan. I love it when he raps (sic).''
Justin - who has just released his new single 'Boyfriend' - replied: ''Seeing that is a huge honor. Yours is a career artists dream of. Congrats on the new album!(sic)''
This prompted Madonna's invite, with her writing: ''Come and join me on stage when I'm on tour when we are in the same city, and congrats on your new single (sic).''
Elsewhere in the chat, Madonna revealed the full extent of her musical abilities. When asked if she can play any instruments besides guitar, replied: ''well i can play The Drums. and i tried playing violin (sic).''
The singer also said she has been listening to a lot of dubstep musician Skrillex, wants Quentin Tarantino to direct a video to her track 'Gang Bang', and she has broken her index finger on her left hand during rehearsals for her tour.
She wrote: ''yes. I have a broken finger. I broke it the other day. My pinky just at the top (sic).''
Madonna, 53, is also looking forward to enjoying an alcoholic drink when her tour starts on May 29 in Israel.
Asked if she'd had a cold beer recently, she replied: ''Not recently. I drank more beer when I lived in London. I won't be having a drink until tour.''