Spanish website Fichajes.net (h/t George Bellshaw of Metro) claim the German international has doubts about his future with Rafael Benitez as the new Galacticos coach, with United set to pounce for one of their long-term primary targets.
Bellshaw says Kroos feels less valued by Benitez, with Red Devils boss Louis van Gaal considered a huge fan of the midfielder.
The 25-year-old was a permanent fixture for Los Blancos during his first season in the Spanish capital. He played 47 times for his new club in La Liga and the Champions League, according to WhoScored.com, with only one of those appearances coming from the bench.
However, the new coach doesn't appear to be as much of a fan of Kroos as previous boss Carlo Ancelotti, with ESPN's Dermot Corrigan explaining why:
Kroos is a more cultured midfielder than he is a destroyer, and Benitez might be looking for more of a physical presence to sit in front of his back four.
However, Opta highlighted the player's key strength, which was on display in the Champions League against Malmo:
Kroos is still young enough to develop further, and for Madrid to allow him to go at this stage appears incomprehensible.
However, Benitez will build the next incarnation of Los Blancos in his own image, and players of Kroos' ilk might not fit the manager's profile for the German's midfield role.
Chelsea To Challenge For Neves
As United prepare a move for Kroos, Madrid could be about to miss out on a potential replacement in Porto prodigy Ruben Neves.
Simon Johnson of the Evening Standard says Premier League champions Chelsea will make a multimillion-pound move to capture the midfielder ahead of Real and Barcelona.
The 18-year-old has stunned the football community with his mature central performances, starring for his club in the Champions League.
If Kroos does decide to leave the Bernabeu for Manchester in the coming months, Neves would be an obvious choice to replace him, but they would have to beat the west London club to the punch.
Johnson says Neves has a £29 million buy-out clause in his current deal, but the Blues are not keen to do business at that price.
It will be an interesting few months to see how Benitez uses Kroos in La Liga, but a player who keeps possession as well as the German does should be an asset to the Spanish coach.
Neves would be a huge gamble for any top club at present, with his buy-out set high to put off suitors, but Madrid will not want to be gazumped by a major European rival for the signature of one of the world's most promising youngsters.