I would be looking to buy direct competition for Mahrez (but possibly the other flank) and a Vardy-esque Ulloa competition, both players who could slot in to their system quickly/seamlessly.
They said they aren't looking to spend in Jan, but fuck it, why not? As a player in that team, I would be looking for ambition from my club, belief we could genuinely make an upset. Try and get Champs league, at least. I'm sure it's where Ranieri sees himself.