The 32-year-old midfielder will soon be entering the final year of his contract at the Santiago Bernabeu and he allegedly has no interest in signing an extension.
According to Todofichajes, Guardiola is 'very aware' of Kroos's situation at Los Blancos and the Spanish coach would be open to the prospect of working with him at the Etihad Stadium.
Should the Germany international inform Real Madrid of his desire to leave this summer, the report adds that the Spanish giants are prepared to sell him for €20m (£17m), although this figure could be reduced to as little as €10m (£8.6m).
During his time in charge of perennial Bundesliga winners Bayern Munich, Guardiola briefly worked with Kroos in the 2013-14 season, which saw the pair win a domestic double.
Kroos – who has also been linked with Man City's rivals Manchester United – is believed to be contemplating his future in the Spanish capital, following the arrivals of Eduardo Camavinga and Aurelien Tchouameni over the last 12 months, the latter of whom arriving this summer for around €80m.
Since joining Los Blancos in 2014, Kroos has made 364 appearances for the club across all competitions and has won 17 trophies, including four Champions Leagues and three La Liga titles. body check tags ::