Last month, Spanish television show El Chiringuito reported the former Bayern Munich star had asked his agent Volker Struth to find him a new club, with Manchester United believed to be showing interest.
Although, the Reds could face stiff competition from former club Bayern Munich who are keen to see him make a return to the Allianz Arena, the report adds.
Kroos has made 15 La Liga appearances this term and has four assists to his name but is yet to score a single goal.
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