Bastian Schweinsteiger says Jose Mourinho "was always asking about Bayern Munich" at Manchester United, as speculation grows the Portuguese could take over the reins at the Bundesliga champions.

Bayern parted ways with coach Niko Kovac on Sunday after a 5-1 loss at Eintracht Frankfurt a day earlier left them fourth in the Bundesliga table.

Pressure had been growing on Kovac all season despite his leading Bayern to the Bundesliga title and a DFB-Pokal triumph in his first year in charge.

Meanwhile, Mourinho has been out of a coaching job since being sacked by United in December 2018, with the 56-year-old considered to be among the frontrunners to replace Kovac.

Schweinsteiger played for Bayern between 2002 and 2015 before moving to United, where he played under Mourinho in the 2016-17 season.

He says Mourinho showed a keen interest in Bayern and the Bundesliga, as well as learning the German language in his downtime.

"I can imagine Mourinho in Germany," he told Bild. "I remember he was always asking me about Bayern and the Bundesliga. During our away games, there was always Bundesliga on TV.

"He really knew every single player, even from the smaller teams. He was also learning German.

"He has not worked in the Bundesliga, so I can well imagine that he would be tempted by a commitment in Germany."

Kovac's assistant Hans Flick will oversee Bayern's preparations for their Champions League clash with Olympiacos on Wednesday and Saturday's Der Klassiker against Borussia Dortmund.