The '4 Minutes' icon is allegedly keen to help the teen launch a successful pop career, and may use the duet as a basis to do so.
The pair have recorded a track titled 'It's So Cool', with the popstar currently contemplating whether to feature it on her next studio album or to include it as part of the soundtrack to her new movie W.E.
"Madonna hopes Lourdes will step into her shoes and become one of the biggest female artists in the world," a source told The Sun.
"She's the perfect mentor for her daughter and is keen to assist her first steps into the industry. Lourdes has a great voice and plenty of character - like her mum."
The mother and daughter duo first recorded the track back in 2003, with the original having an acoustic feel, but Madonna had the song reworked back in 2009. It was then included as part of her Celebration greatest hits compilation, with Lourdes's vocals removed.
Lourdes recently revealed that she shares clothes with her mother, despite there being a 38-year age gap.
Listen to Madonna's solo version of 'It's So Cool' below: