If the album makes number one in the UK, she will beat the record currently held by Elvis Presley for the most number one albums by a solo artist.
It would be her 12th appearance at number one, including compilations The Immaculate Collection and Celebration, and the Evita soundtrack.
MDNA has shifted 39,000 copies so far, said the Official Charts Company.
In the US, it is expected to sell 300,000 - 350,000 copies, almost double this week's number one, which is the soundtrack to action movie The Hunger Games.
It will be the pop star's eighth number one album in the US, and the first-week sales will be higher than those of Madonna's last studio album, Hard Candy, which debuted at number one with 280,000 copies sold, according to US chart compilers Nielsen SoundScan.
Madonna still has some way to go to break the record for the most number one albums in the UK. That honour is held by the Beatles, who topped the charts 15 times.
From BBC News