Shilton began his career at home town club Leicester in the 1960s, but it was at Forest from 1977 to 1982 where he won silverware as Brian Clough led the club to the old First Division title, two European Cups and two League Cups.
Leicester's title triumph has provided the greatest shock in domestic football since Forest came out of the old second division in 1977 to become English champions at the first time of asking - and Shilton feels the Foxes are also capable of being more than a one-season wonder.
"They've handled the pressure and proved they're the best team in the country," Shilton, England's most capped international, told BBC Radio Five Live's Sportsweek programme.
"People say they can't sustain it - but why can't they?
"At Forest we won the League Cup the year we won the league and we went on to win two European Cups, another League Cup and a Super Cup.
"That's the next step for Leicester now
Can they prove they're a great team over a number of years?
"There's no reason why they can't in my eyes, they just need to strengthen the squad."
Shilton, however, expects Leicester to stick with the blueprint that has taken them to the summit of English football.
It is an incredible story coming just o ne year after being in the thick of a relegation battle, and two since arriving in the Premier League as Championship winners
"I don't think you'll see them getting someone with a big Lamborghini, flash toilet bag and entourage just because he's a decent player," said Shilton.
"It will be (players in) a very similar mould, down-to-earth family people and good professionals with a fair bit of ability.
"I see them improving the numbers but not changing the make-up of the player.
"Leicester is very reminiscent of what we had at Forest, they can cut teams apart with their football but they can also battle and get a 1-0 win
That team spirit and will to win is what we had."
Shilton said he also recognised similarities between Clough and current Leicester boss Claudio Ranieri.
The 64-year-old Italian was seen as a strange choice by many when he was appointed last summer.
He had flopped in his previous post with the Greece national team and failed to win a national title during his time in charge of some of the biggest clubs on the continent
"There was only one Brian Clough
When he walked in a room everyone knew someone special had walked in," said Shilton.
"Ranieri is slightly different, but he does connect with the players and he's got that personal touch like Brian Clough.
"I saw it in the celebrations with all the families and the backroom staff, it was like a carnival.
"It's what management is about, it's not just about the blackboard, tactics and training.
"It's about connecting with people and establishing relationships with the players
It's about the players respecting you, but also having fun as well."
Source : PA
Source: PA