Sport Mediaset report that Real Madrid will make Pogba, a former-United academy player, their top transfer target heading into next season.
And Carlo Ancelotti's side are willing to commit up to €60m to land the French international. Florentino Perez has a habit of making one big-name player his top target each summer - and he inevitably gets his way.
Gareth Bale was the subject of Real Madrid's advances last year, and the Bernabeu giants hope Pogba will be next.
But Juventus are desperate to keep him at the club. They signed him for nothing in the summer of 2012 from Manchester United, and Pogba has blossomed into one of the top midfielders in world football already.
United and Paris St Germain have been heavily linked with the 20-year-old central midfielder, with David Moyes thought to ready to make a big splash in the transfer market this summer.
But they may find the competition too intense. PSG and Real Madrid have deep pockets, while Juventus look ready to offer him a bumper new deal to persuade him to ignore the suitors.