The Gunners have been made fourth favourites for this season's competition in the prediction.
Opta Analyst's supercomputer simulated the upcoming Champions League campaign 10,000 times to predict the winners.
The 36 clubs involved in the league phase have also been given percentage chances of reaching the last 16, quarter-finals, semi-finals and final.
This season sees an overhaul of the Champions League, with the group stage replaced by a league phase.
A top eight finish guarantees progression straight through to the last 16, with the clubs ranked ninth to 24th going into a play-off round.
The remaining eight clubs in 25th to 36th are eliminated from Europe and no longer have the safety net of the Europa League.
League phase action gets underway on Tuesday, with matches spread across three nights this week.
Ahead of the opening matchday, Opta Analyst's supercomputer has given Arsenal a 6.3 per cent chance of lifting the trophy for the first time.
Mikel Arteta's side have also been given a 13.2 per cent likelihood of making the final at the Allianz Arena in Munich on May 31.
Meanwhile, their chances of making the last 16 are 76.5 per cent following a run to the quarter-finals last term.
Arsenal begin their campaign away to Atalanta on Thursday before facing Paris Saint-Germain, Shakhtar Donetsk, Inter Milan, Sporting Lisbon, Monaco, Dinamo Zagreb and Girona.
The supercomputer has ranked three clubs ahead of Arsenal in their predictions, with Manchester City the favourites.
Pep Guardiola's side have been handed a 25.3 per cent chance of reclaiming the title they won in 2023.
Defending champions Real Madrid are the next most fancied side at 18.2 per cent ahead of Inter with a 10.9 per cent chance.
As for the remaining English clubs, Liverpool are predicted to have a 4.2 per cent chance of winning their seventh European crown.
However, Aston Villa are unfancied at 0.2 per cent on their first appearance in the competition since 1983.
The supercomputer has also given nine clubs a 0 per cent chance of winning this season's Champions League, with Celtic amongst them.
