The former England striker, who won the league with Blackburn Rovers in 1995, had just watched the Foxes ease past the Gunners thanks to goals from Jamie Vardy and James Maddison to move one place off the top behind leaders Liverpool.
And Shearer believes Leicester, who equalled the Premier League record win with a 9-0 win against Southampton last month, have the firepower to challenge for a repeat of their historic championship win in 2016.
"Yes, they are [title contenders],” the former Newcastle captain told Premier League Productions. “Because every single week, when they get the results, you’ll see the manager and the players trying to straight bat it and say ‘no, we’ve got no chance’.
“The longer they keep saying that, the longer everyone else keeps saying that, the better they’ll keep on creeping up. Yeah, they’re in it. We’ve said this before.
“They can’t keep it up. There’s no way they’ll stay in the top. We’ve said it before and learnt our lesson. It came back to bite us all as pundits. They stayed there, with that team, with a little bit of luck they can stay there as well.”
Leicester are five points behind leaders Liverpool, though the Reds have a game in hand ahead of their fixture against champions Manchester City on Sunday.
The Foxes are a point clear of City and will retain their place in second through the international break if Pep Guardiola's side lose to Liverpool.
“Let’s look at the so-called who we expected to be there before the season started,” said Shearer. “Tottenham. Are they better than Tottenham? Absolutely. Arsenal? Absolutely. Chelsea? Maybe on a par with them.
“There were a few people suggesting that Leicester could actually get into the top four. This Leicester team have proven that they can do that."