Former France international Frank Leboeuf had suggested the Swede become PSG captain ahead of Thiago Silva, who he said had an "attitude problem".
Speaking at a news conference on Friday, Blanc talked up Ibrahimovic's qualities but said he was just one of several leaders in the Ligue 1 champions' squad.
"Ibra is a leader in the team. Nothing very surprising, he's been a leader in his previous teams as well," Blanc said.
"I speak also on the pitch because he's a technical leader. He's a natural leader, natural within the squad due to his personality and character. He's not the only one.
"Saying that he's the boss of Paris Saint-Germain is offensive to the board and the head coach that I am.
"The boss of the team, yes, but the boss of PSG would mean that the guy is taking the decisions for everything which is not the case, even if of course it is important.
"He's an important player within the squad we cannot deny it and I am not going to deny it. Really not. He's one of the three to four natural leaders within the group."
PSG face Guingamp in the Trophee des Champions on Saturday, and Ibrahimovic said his side were keen to better their three-trophy haul of last season.
"I know there's a lot of pressure on us but many of these players that are here today, they like to play under pressure and they're used to the pressure," he said.
"[We'll] just continue to train hard and to try to win the games we need to win. We know what we need to do and what happens in the end, we wait and see.
"It's not only about being a strong team. You need to go out and demonstrate also that you're a strong team. Every day in training and also every game that is coming."
