How much is 'big'? £50 million for a player?
£50 million players don't want to come to Leicester. They want to go to one of the 'big' clubs.
If Harry Maguire was at another club, he wouldn't come to Leicester now. Not now he's a £60M+ player.
If Mahrez and Kante had been at Southampton, for example, there's no way they'd sign for Leicester when bigger clubs wanted them.
The way we end up with players worth £50 million, is by signing them for less, and turning them into more valuable players. Either because our scouts have spotted something others haven't, or by taking a chance on a young player with potential.
The only way we'll be able to sign top players is by becoming a big club. And that doesn't happen overnight, even if you have won the league.