The Gunners sit top of the Premier League and Champions League tables, while also are into the Carabao Cup final and alive in the FA Cup.
On a clean sweep, Pennant told Tribalfootball.com: "It's so difficult to do. But listen, if you're in the four competitions, it's realistic. If you're in it, then there's a chance. There's no reason.
"You're top in the Champions League group. You won with a perfect record, 8 from 8. So you've got every right to say, 'look, yeah, we can win the Champions League'.
"It just depends how much of the league run takes out of them as well because we saw liverpool in the same situation you know going for the league also trying the Quadruple and ultimately trying to fight on all four fronts.
"It does take it out of your players and you can come across injured key players and ultimately you know you end up sacrificing a few competitions."
On Kai Havertz's return to full fitness, Pennant says the timing couldn't be better.
He added, "I think Arsenal needed him.
"So yeah, they need someone upfront who they can rely on. And last season they did rely on Kai Havertz, you know, not only with his goals, but with his assists as well, what he used to chip in with.
"Yeah, he can hit the ball, you know, his all-round game is great. He's got hold-up play. He can create goals by himself, you know, you name it. So that's what you kind of want. So having him back is an absolute massive boost for Arsenal for this title."
- Jermaine Pennant was speaking to Tribalfootball on behalf of BetSelect