Cigarini is expected to leave Napoli after failing to impress coach Walter Mazzarri.
The midfielder has been linked with a move to Spanish side Sevilla in recent weeks.
But Parma president Tommaso Ghirardi has admitted they would like to see Cigarini return to the club.
Ghirardi told Mediaset: “I’d like to have Cigarini here again. He hasn’t been given the space that he needs at Napoli to express himself.
“He would definitely have that space with us. If he wants to come back here then we will wait for him.”
