O'Neill said Mignolet is going nowhere - and reasserted his desire to add "quality" to his squad in the January transfer window.
"We wouldn't want to lose any of our key players next month," he said. "I haven't heard of any specific interest, but I certainly wouldn't want to lose Mignolet or any of the other players who have been so important to us so far this season.
"He's been outstanding for us so far, so he's definitely not someone we would want to see leave.
"I haven't heard of that (the Arsenal link), but I'm not in any position to let our good players go in January. I think we've really got to be looking to try to improve our squad next month."