The Gunners go into Wednesday's Champions League last 16 second leg clash at Camp Nou needing to score twice to have any chance of progressing, having lost 2-0 at the Emirates Stadium in the first leg.
And Hartson believes his former club would have to cause one of the biggest upsets in the history of the competition to progress at the expense of Luis Enrique's side.
“Arsenal have no chance, even if they played with 16 players on the pitch at the same time against 11 they would not go through," Hartson told Goal.
“I am not being disrespectful, that is just the gulf in class between the sides.
“Of course, I would love Arsenal to prove me wrong. I love the club, I love Arsene Wenger. I was in his first Arsenal team when he took over in October 1996 and I speak to him regularly.
“But there is no escaping it would probably be the biggest shock in the history of the Champions League if Arsenal pull it off. I’d probably put the odds at 50-1 they can overturn the deficit, but I’m not going to waste my money.”
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According to Hartson, Arsenal have to "hope for a miracle" after a double in the first leg from Lionel Messi, who along with Luis Suarez and Neymar will be confident of putting the tie well out of reach of the Gunners at Camp Nou.
He added: “It might only be a two-goal deficit, but if Arsenal were to have any chance they needed to get a lead and a clean sheet at the Emirates.
“They played well for an hour, but an hour isn’t good enough and I don’t think Barca were at their best.
"Arsenal cannot afford to go after it because they will be exposed at the back. Messi, Suarez and Neymar will fancy their chances against a defence that has leaked too many soft goals.
“They need to keep it tight, take any chances that come their way and hope for a miracle.”
Arsenal boss Arsene Wenger appears to be running out of opportunities to win the Champions League, with some sections of the Gunners support calling for the Frenchman to leave the club, but Hartson does not think failure to win Europe's top competition would damage his legacy at the Emirates Stadium.
“It does look increasingly likely that he is not going to win the Champions League, but that should not detract from his achievements in the competition,“ Hartson said.
"To reach the knockout stages 16 years in a row is amazing and has helped put the club on the map in Europe and beyond.”