Reports in Italy have suggested that Stramaccioni will leave the club in the summer following a disappointing campaign by the Nerazzurri's standards.
Inter are currently in seventh place in the Serie A table, while recent exits in both the Europa League and the Coppa Italia have heaped further pressure on the coach.
"You will know the future of Stramaccioni on June 30," Goal.com quotes Moratti as saying. "At the moment it is difficult to judge his actions as we have been hampered with injuries."
Inter resume their league campaign on Sunday when they welcome Parma to the San Siro.