Indonesian businessman Thohir has made no secret of his ambition to return Inter to their status as one of the biggest clubs in the world following his takeover of the Serie A side last October.
They are sixth in the table, a mammoth 31 points behind runaway leaders Juventus with nine matches remaining.
Mazzarri was only appointed 10 months ago and although Thohir stated that he is not planning a change of coach, the 43-year-old offered no guarantees over the futures of the former Napoli man, sporting director Piero Ausilio and chief executive Marco Fassone.
When asked if he could be sure that the trio will still be at the club next term, Thohir told Gazzetta dello Sport: "No, because everybody is under scrutiny. Even (Michael, chief financial officer) Williamson, who I wanted at the head of HR, finance and legal issues, is under scrutiny. It's fair trusting everyone, but everybody has to be responsible for his actions.
"I don't want to be misunderstood: at the moment I'm very happy with the work of the three people you mentioned. But I keep checking up on everyone."
Thohir has already showed his ambition by securing the signing of Manchester United captain Nemanja Vidic for next season, while key duo Fredy Guarin and Rodrigo Palacio have signed new contracts.
