However, Hoffenheim spokesman Markus Sieger insisted Saturday: "We can't and won't comment for the moment."
The 52-year-old's contract runs until June 30, 2012 after extending last May. Rangnick took over in June 2006 and under his guidance the small outfit from southern Germany reached third in the Bundesliga.
Bayern Munich announced earlier Saturday that Hoffenheim's Brazilian midfielder Luiz Gustavo had agreed a move to the Bundesliga champions with immediate effect, a transfer which Rangnick totally opposed.
"The departure of Luiz Gustavo to Bayern during the winter break is out of the question in my eyes," Rangnick said last month.
Hoffenheim are currently eighth in the Bundesliga.
Hoffenheim have now appointed his deputy Marco Pezzaiuoli as coach, who takes over with immediate effect, the club said Sunday. Pezzaiuoli, 42, played for Mannheim before going into coaching with Karlsruhe.