The 24-year-old midfielder has turned down Bayern's offer of a contract extension and he stated prior to the World Cup that he needs to know where his future lies.
According to Sport1 television, that could well be in the Primera Division with the Germany international reported to have already agreed terms on a five-year contract with the Champions League winners.
All that remains now is for the two clubs to reach an agreement over a transfer fee which would see Kroos join compatriot Sami Khedira in Real's midfield next season.
Kroos only has 12 months left to run on his contract with Bayern and, since he has refused their offer of an extension, the chances of them cashing in on him this summer are high.
Manchester United are also understood to be interested with their new coach Louis van Gaal having already worked with Kroos for two seasons at Bayern.
- Sports & Recreation
- Sami Khedira