Arsenal have been pushed out from 25/1 to 40/1 in Sky Bet's Champions League outright odds after being handed a difficult draw.
The Gunners, who were seeded in the first pot for the draw, were placed in Group F alongside Marseille, Borussia Dortmund and Napoli and are second favourites to qualify in top spot behind last season's runners-up.
Bayern Munich remain the favourites at 7/2 followed by Barcelona (9/2) and Real Madrid (11/2), while PSG and Juventus are considered the best of the rest at 18/1 apiece.
Celtic's price has been pushed out significantly, from 400/1 to a hefty 1500/1, after they were placed in the same group as Barcelona, AC Milan and Ajax.
Sky Bet Football Trader Chris Spicer said: "Arsenal were already considered a far longer price than the other Premier League sides having failed to strengthen in the transfer market this summer, but now they face a tough task in even making the knock-out stages.
"However, their impressive record of making it through the groups stages warrants respect, so we make them marginally odds-on to progress, certainly a better chance than poor Celtic."