Hooper, who has scored 18 goals this campaign, has been linked with a January departure in recent times but Parker is hoping he can stay at Parkhead and help the Glasgow giants defend their Scottish Premier League title and go as far as possible in the Champions League.
"Would it be madness for Gary to leave now? Of course it would," Parker said.
"I expect him to still be here at the end of January, definitely. We want to keep him.
"We have the last 16 of the Champions League coming up, so I don't think any player would like to leave now.
"I don't know what his thoughts are, but I think he will stay.
"It's down to the manager and the people upstairs. But why would he want to leave when he has Champions League football?"