Leicester are currently 16 points clear of third-placed QPR in the Sky Bet Championship and could clinch promotion back to the top flight as early as this weekend if results go their way.
Davies, who made 470 Premier League appearances for Southampton, Blackburn and Bolton, believes the Foxes will go from strength to strength.
He told Sky Sports News Radio's FL72 Weekly show: "Leicester for me have got by far the best squad and best side in the league.
"I think when they go up they can become an established side in the Premier League, similar to a club like Southampton, who with the backing and the investment can bring in four or five quality players. I expect them to do really well in the Premier League.
"They have the pace and the power and the strength. There were a few doubts over whether Nigel Pearson could do it - I was one of those people who were unsure - but he's done a terrific job and they've been the best side and the most consistent side in the league.
"Burnley under Sean Dyche have been brilliant with their squad. You look at the difference between the two squads and Dyche if he can get them over the line will have done a fantastic job to get them back into the Premier League but I think Leicester can do really well."
Scunthorpe midfielder Dave Syers, also on this week's FL72 Show, agreed, adding: "I think all season Leicester have shown themselves to already be a Premier League outfit.
"The way they have steamrolled teams week-in, week-out throughout the season, they've not shirked it when they've had those big games against the likes of Burnley when they've had to win.
"I think with maybe two, three or four quality signings which they do have the financial backing to go out and get, they'll be a very strong Premier League team whereas Burnley, if they get over the line, will have to strengthen a lot more."
You can listen to the full FL72 Show via the Soundcloud player below.