“He's an extraordinary player that I dream of seeing at Parma, but today we can't afford him," Faggiano told the Guardian.
AC Milan remain favourites to sign Ibrahimovic.
Faggiano also spoke of signing former Arsenal striker Gervinho.
“The story is incredible. One day his agent came to our office and offered him to us. I discussed it with my staff. 'Really, that Gervinho?'
“There was some scepticism since he hadn't been in Europe for a while, but it was a deal we could take a risk with.
“Someone, who is no longer at our club, tried to get in the way since they didn't want him but I had made up my mind. I believed in it a lot.
“Some teams wanted him. But he stayed because he feels part of our family; this makes you understand what Parma is all about."