Ayew has been linked by British media with possible moves to Sunderland or West Ham United.
"I hope he stays. I don't know, but we have discovered other good characteristics with him," Guidolin told British media.
"He says he is not a striker and he is a midfielder but in my opinion he is a striker. He is also a good false nine.
"He is a big player, but his attitude is good. He is an important player, but he is quiet, a good guy."
(Reporting by Ian Rodricks in Bengaluru; Editing by John O'Brien)