Kroos has been a long-term target for the Red Devils and had agreed to join them in 2013 while he was at Bayern Munich, but later changed his mind.
He then signed for Madrid and has gone on to win three Champions League titles and one La Liga trophy.
The Sun report that the 29-year-old is keen to reignite his career elsewhere after a disastrous season with the Spanish club.
The German international has not scored and has just three assists this season.
He is under contract until 2022 but has made no secret of his desire to play in the Premier League.
Kroos was on the verge of joining United in 2013 and they had an agreement in place, when David Moyes was the manager, but the Scot’s sacking led to the deal falling through.
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He then went on to move from Bayern to Madrid for £27million in July 2014.
Paris Saint-Germain are also reportedly interested in Kroos and are lining-up a £68million bid, according to the Daily Mail.
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