Celtic finished third in their Champions League group, collecting just three points after losing all four meetings with European giants Bayern Munich and Paris Saint-Germain.
Their better head-to-head record over Anderlecht meant they finished above the Belgian side and drop down to the Europa League.
Ahead of tonight’s home clash against BATE Borisov (8.05pm), Arsenal have already won Group H and are a potential opponent for Celtic in Monday’s draw.
Keown says Celtic need a good run in the competition to restore some credibility for the Scottish Premiership.
“Napoli are a decent side, Celtic, I would love to see them play, maybe against Arsenal,” he told BT Sport.
“I think just for the credibility of their own Scottish division, they need Celtic to do well.
“They didn’t do well in the Champions League. It starts to hot up, Atletico Madrid of course will fancy their chances.
“Arsenal, of the teams currently in the Europa League, have probably been the best team.
“But when these teams drop out of the Champions League, it’s going to get tough now.
“We’re into the last-32 as opposed to the Champions League which is into the last-16.
“It’s more hurdles to jump over but I feel in February the teams will really start to play their strongest teams.
“Arsenal haven’t done that up to now and I expect them to do that later in the tournament.”