The former German international is yet to feature for Los Blancos during their unbeaten start to the 2021/22 season due to a persistent groin injury.
Kroos is rumoured to have played on through the pain in the final weeks of last season, and in Euro 2020 this summer, before eventually breaking down in August.
According to reports from Marca, the midfielder took part in his first session this season earlier today, with the club’s medical team monitoring his progress in the coming days.
Estimates over his possible first team return remain unclear at this stage but initial indications hint at another two weeks of training.
He could be fit in time to face Espanyol on October 3 but Ancelotti may opt for caution and give him the next international break to build up an additional layer of fitness.