According to Swedish reports, the singer is negotiating a multi-million pound deal to front the Scandinavian clothing firm.
The country's Daily Expressen newspaper said: "She's a superstar, a style icon, and controversial. Madonna could be H & M's next clothing model."
The 47-year-old mum of two will be the latest in a long line of stunning star women to front ad campaigns for the popular high-street chain.
Previously, Kate Moss, Naomi Campbell, Cindy Crawford and Anna Nicole Smith have all advertised the brand.
The firm also boasts successful collaborations with high-profile designers such as Madonna's close friend Stella McCartney - her capsule collection sold out in minutes and caused chaos as fans scrambled for cheap off-the-hanger pieces.
H&M have recently announced they will launch a special collection created by Dutch design duo Viktor + Rolf in November.
It is believed Madonna appear in the accompanying advertising campaign.
Company spokeswoman, Kristina Stenvinkel, would neither confirm nor deny the reports, saying: "Our policy is to never comment on such speculation."