The Frenchman, who played for both clubs in a glittering career, expects the Gunners to at least hold off Tottenham in the race for fourth place ahead of the north London derby.
“Although it depends on what Chelsea do, [Arsenal] can reach third place as well,” Petit told Genting Casino.
“When I saw Chelsea, on my last visit to England, what’s going on inside the club, then on the pitch as well, I think most of the players are showing tiredness, mentally and physically.
“It’s a hard end-of-season for them, but I’m pretty sure they will finish in a Champions League qualifying spot. Every single player in this team knows how important it is to be in the top four next season.”
Petit questioned how Chelsea found themselves in a situation where their defence in particular is crumbling under the uncertainty of the takeover situation.
Unable to offer new contracts to players until Todd Boehly’s purchase of the club goes through, the Blues are set to lose Antonio Rudiger and Andreas Christensen on free transfers in the summer – with Cesar Azpilicueta potentially joining them.
He continued: “One thing I don’t understand about Chelsea is when you’re a big club, you’re expected to do things and I can understand if it’s one or two players but there are so many players that don’t know if they are going to be a part of Chelsea in the future.
“The takeover may be done but it doesn’t mean the players know anything about their contracts, especially in defence. For the last two seasons, Chelsea have bought so many players up front, because they were missing strikers, and now they have to revert to their old defence. This is something I don’t understand with Chelsea.”