Bayern's Kane in frame for Dortmund after return to individual training
Bayern issued a statement saying the 30-year-old striker "completed an individual session at Bayern's training ground on Monday morning".
Kane was subbed out after injuring his ankle in Bayern's 5-2 win over Darmstadt and missed England's 1-0 loss to Brazil on Saturday.
He travelled back to Munich for treatment on Sunday after England manager Gareth Southgate said the forward would not be fit for Tuesday's friendly against Belgium.
The England captain has a history of ankle issues but has not yet missed a game in the league for Bayern this season, where he has scored 31 goals in 26 games.
Bayern did not reveal whether Kane would be fit to face Dortmund on Saturday.
Winners of the past 11 Bundesliga titles, Bayern sit 10 points behind league leaders Bayer Leverkusen with eight games to play this season.
Bayern have been drawn to face the former Tottenham striker's ex-rivals Arsenal in the quarter finals of the Champions League, with the first leg taking place in London on April 9.
Bayern's Raphael Guerreiro, Kingsley Coman and Noussair Mazraoui also returned from injury to take part in individual sessions on Monday.