The 'R.I.P' singer is said to have been suggested for the role by the Queen of pop's daughter Lourdes.
Madonna: "Lady Gaga Reminds Me Of Myself"
The '4 Minutes' singer described the 'Marry The Night' star as "very talented' during a recent interview.
Madonna has described Lady Gaga as "cool" and says the 'Born This Way' singer reminds her of herself when she was just starting out in the music industry.
The 'Music' singer made the comments during a pre-taped appearance for The Graham Norton show which was filmed earlier today (11th January).
"When I first saw her I was really impressed by her and she was cool," Madonna told host Graham Norton during the interview. "She did remind me of me back in the day."
Madonna added: "I do think she is very talented."
Earlier today Madonna announced her tenth studio album, due to be released later this year, will be titled 'MDNA'.
In December Nicki Minaj and M.I.A. filming the music video for Madonna's lead album single 'Gimme All Your Luvin', after both contributing guest vocals to the new track.
Madonna's appearance on The Graham Norton Show is due to air on BBC1 this Friday (13th January).
The 'Give Me All Your Luvin' singer is said to have agreed to forget about her disagreement with the UK star.
Madonna thrills fans as she brings her 'MDNA' world tour to London for a huge outdoor show in Hyde Park.
Watch the Queen of pop's latest release from her 'MDNA' album right now on Capital.