According to information from Bild, there have reportedly been "considerable concerns" inside the club since pre-season over whether Demichelis has the right approach for Leipzig's style of play.
Club bosses reportedly felt the 45-year-old had shown too few ideas in possession over the course of his coaching career so far.
That showed last weekend, among other things, when Leipzig struggled to create dangerous chances against a defensively well-organised Werder Bremen. "Our occupation of the box was not good enough. Against an opponent sitting very deep, we found too few solutions," said sporting managing director Marcel Schäfer.
After the 3-1 defeat at SVW, Schäfer called it a "real wake-up call" and said the club now had to draw the right conclusions immediately. "We do not need to single out individual players, I expect a clearly different performance. With our own standards, we cannot simply brush this game aside."
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How long did Martin Demichelis sign for at RB Leipzig?
Demichelis only took over as head coach of the Saxony club last summer, replacing the sacked Ole Werner. Before that, the former Bayern Munich defender had been working at the relegated Spanish club RCD Mallorca.
To land the Argentinian, Leipzig are even said to have triggered a release clause in Demichelis' contract. His deal at RB runs until 2028.
Leipzig opened the Bundesliga season with a 3-0 win against Borussia Mönchengladbach. They also cruised through in the DFB Cup, beating Regionalliga side Eintracht Trier 6-0 as expected.