Both players have been linked with moves to the Italian champions following a season of controversial moments both on and off the pitch.
Milan tried to sign Tevez on a loan basis in January and were thought to be considering renewing their interest at the end of the season.
However, when asked about Tevez, Galliani replied: "I don't know who he is."
Meanwhile, the vice-president has also denied that he has held discussions with Balotelli, who once played for rivals Inter Milan.
"No, we don't hear from each other and even if we did I would not tell you," Galliani added.
Milan are currently second in the Italian league.