Vucinic is said to be unhappy in the capital and there are reports that he will seek a move elsewhere in the summer.
"I have read that Mirko is playing badly because he wants to leave," Alessandro Lucci said. "The time has arrived for a clarification.
"In January, for reasons outside of football, we spoke to President Sensi and the directors to understand if we could find an [alternative] solution.
"However, on that occasion they confirmed to me his importance to the group. Mirko stayed without a problem.
"He is happy in Rome. He has another two years left on his contract. He has never asked for a pay rise as has been reported."