Jose Mourinho has long been an admirer of Kroos and wants him to partner Paul Pogba in the heart of Manchester United's midfield.
And according to Spanish outlet Diario Gol, the 27-year-old would consider leaving the Bernabeu in favour of joining up with his former boss if Madrid end the season empty handed.
The Spanish giants were knocked out of the Copa Del Rey earlier this year and have surrendered their lead in La Liga to Barcelona.
Toni Kroos is reportedly unsettled at a lack of trophies at Real Madrid
Jose Mourinho is keen on bringing Toni Kroos to Old Trafford
Madrid do hold a commanding 3-1 lead ahead of their Champions League last-16 second-leg tie against Napoli tonight.
But no team have won Europe's elite competition in back-to-back years since 1978.
Former Manchester United boss David Moyes claimed an agreement was in place for Kroos to move to Old Trafford in 2014 prior to his move from Bayern Munich to Madrid.
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David Moyes said an agreement to sign Kroos at Man United was in place in 2014
“Toni Kroos was agreed to come in the summer," Moyes said last year. "I had agreed it with Toni himself and his agent.”
The 2016 Champions League triumph has been Kroos' only major trophy that he has lifted in his time at Madrid along with the 2014 UEFA Super Cup and two FIFA Club World Cup's.