D'Amico arrived in Scotland on Thursday to kick off talks with with Charles Green, who is leading the consortium in place to take over the Ibrox club, and director of football administration Andrew Dickson, although whether Gattuso becomes a Rangers player again will depend on the lifting of the transfer embargo and on exiting administration.
D'Amico told the Daily Record: "It is Rino's wish to come back to Rangers but first I have to speak to the people at the club to find out what the situation is. He knows all about the Rangers financial situation. We know it is difficult but we can work to find a solution."
He added: "Rino talked with Ally on the telephone. They know each other very well and like and respect each other. Now we have to work to see if something can happen.
"Not being in Europe next season would not be an issue for Rino.
"I will meet with Rangers again tomorrow for further talks."
Green confirmed he had met with Gattuso's agent and added: "Fans should be aware of just how big the club is when one of the greatest players publicly states he wants to finish his career at Rangers at a time when we can't sign anyone.
"He has confirmed he wants to play for Rangers and that is something we could do if we were able to sign someone."