The Milanese club currently sit fifth in Serie A, 16 points adrift of leaders Juventus, and were eliminated from the Coppa Italia in the round of 16.
While offering Mazzarri his backing for the time being, Thohir admitted the duo would meet to re-evaluate the situation in the coming months.
"So far, I say 'yes, it is the right coach' and I believe in him," he told Corriere dello Sport. "Before the end of the season will meet him to see if his vision coincides with that of the board of the company."
And Thohir expressed a desire to return the club to its former glories, reiterating his joy at being involved at San Siro.
"When I see the glories of the past Nerazzurri I get excited," he continued. "I never imagined to be a partner of (Massimo) Moratti and to become the owner of the club, but had the opportunity, I did not think twice.
"I am here because I want the good of Inter, to bring this club to be competitive and to win. I do not mean to put too much pressure on the players.
"I'm happy to be here. I enjoy doing what I do."
Inter visit second-placed Roma in the Italian top flight on Saturday.
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