Reports on Thursday suggested the England international was ready to quit Arsenal, with Palace at the front of the queue to sign him.
He has yet to break into the Arsenal first team this season in the Premier League and a January move could be on the cards but Hodgson has denied they are discussing a deal.
The former England boss has refused to rule out a move in the future but he insists nothing has been mentioned in recent talks with the board.
He told reporters: "Who has linked him? That's what you need to find out, because it didn't come from us.
"I will tell you who, his agent -- because that's where newspapers get their stories from.
"We have never mentioned his name. I work with Dougie Freedman and we talk about potential players, and Jack Wilshere's name has never been mentioned in this room.
"I like him and I think he is a very good player. There may come a time at Crystal Palace where Jack Wilshere would be just the player we are looking for, but I can't tell you that is the case at the moment."