The striker was watched by Norwich boss Chris Hughton as he struck the only goal of the game in Thursday's 1-0 defeat of Motherwell and has been linked with a number of clubs with the January transfer window now open.
The win stretched Celtic's lead at the top of the Scottish Premier League to nine points, while they host Juventus in the first leg of their UEFA Champions League last-16 clash next month.
Parker said: "I expect Gary to be here at the end of January, definitely.
"Would it be madness to leave now? Of course it would.
"We want to keep him. We are in Europe, the last 16 of the Champions League is coming up. 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. I'm certainly hoping that.
"It's down to the manager and the people upstairs - but why would he want to leave when he has Champions League football?"