The Ligue 1 club have taken the decision despite the fact that the Italian guided the Red and Whites back into France's top flight in 2013, before leading them to the runners-up spot behind champions Paris Saint-Germain last term.
Speaking at a press conference, sporting director Vadim Vasilyev said: "It was a difficult decision. It is not clear when the results are very good. We are looking for a coach who has an offensive vision and can make a good show."
Reports have claimed that current Sporting Lisbon boss Leonardo Jardim is the leading contender to replace Ranieri.