The Foxes currently sit fourth in the Premier League.
They are only a point behind the Gunners while the Blues are only behind on goal difference.
This is the highest position Leicester have been in since their promotion five years ago.
While United have suffered a poor run under Ole Gunnar Solskjaer .
And Walsh, who made more than 350 appearances for the Foxes, believes Brendan Rodgers’ side have a chance to break into the top four.
Speaking exclusively to Starsport, the former defender said: “The one thing we’re not doing is getting too carried away.
“In football, things can change at one moment.
“But there’s a great vibe around the city and team.
“There’s an opportunity this year.
“United are out of sorts, Arsenal at the back are vulnerable, Chelsea have an embargo.
“There’s an opportunity to break through and Leicester could do that.”
The 54-year-old went on to make a big claim about the Foxes.
He added: “If they continue the way they’re playing, I do believe they’ll get better.
“There’s some class players and good squad big enough to rotate.”
Walsh previously singled out one player in the Leicester squad who has impressed him.
“It’s been a great team effort but I’d look at Ricardo Pereira,” he said.
“He’s been nothing short of excellent.
“There’s more to come form this team I think.
“Maddison’s been a revelation and hopefully he’s fit to play.”
It comes as James Maddison has been warned about being labelled a “spice boy” .
The Foxes sit 10 points behind league leaders Liverpool, who hope to continue their 100 per cent record against United.