The singer said she approached the UK star to join her on stage at the Lucas Oil Stadium, Indianapolis back in February, but Adele had to decline due to her voice recovery.
Asked if she would like to work with Adele, Madonna told ITV1's Daybreak: "Yes, I would love to. I would love to meet her, I think she's brilliant, I love her."
She added: "I wanted her to be in the Super Bowl with me, but I think she was having her throat problem or throat operation or something."
Madonna was eventually joined by LMFAO, Nicki Minaj, MIA and Cee Lo Green for renditions of 'Vogue', 'Give Me All Your Luvin'' and 'Like A Prayer' among others.
Madonna will embark on her new world tour in support of latest album MDNA in May and has told fans to expect "amazing music and incredible dancing".
> Madonna 'doesn't know who One Direction are'
Watch Madonna's Super Bowl half-time show below: