The veteran German international clinched his fourth Champions League title with Los Blancos last month, and his fifth overall, after success with Bayern Munich in 2013.
However, the 32-year-old paused contract extension talks, to allow for some thinking time this summer, as he enters into the final year of his current deal.
Los Blancos are flexible over offering him a possible 12-month extension in the coming months but the decision has been left in the hands of the former Bayern Munich star.
As per reports from Cadena SER, via Diario AS, Kroos will not sign a renewal, and will end his time in Madrid in 2023.
Kroos has insisted he wanted to base his decision on still playing a key role in the Real Madrid midfield and the summer arrival of Aurelien Tchouameni indicates a look to the future.