Kroos' future has been the subject of intense speculation for some time, with the 24-year-old out of contract at the Allianz Arena at the end of the upcoming season.
He was a central figure for Germany as they won the World Cup in Brazil, starting all seven of their matches and contributing two goals – both scored in their 7-1 semi-final humiliation of the hosts.
And having previously stated his desire to join Real, Kroos has now hinted that confirmation of the switch could be just around the corner.
"Tomorrow or the day after I will go to Madrid," he is quoted as telling Spanish newspaper AS while holidaying in Majorca.
Kroos, who has also been linked with a move to Manchester United, made 49 appearances for Bayern in all competitions last term, scoring four goals.
His signing would represent Real's first plunge into the transfer market this season as they look to launch an assault on the Liga summit, having finished third last term.
Carlo Ancelotti's side will also have their UEFA Champions League crown to defend, as well as a hectic schedule due to their involvement in the FIFA Club World Cup.
