Walker joined AC Milan from Manchester City, while Kolo Muani left PSG for Juventus.
Ranieri revealed today: "We've put together a fantastic scouting group. We cover the whole world. I said what I think the future holds for us based on the players and these guys bring me 4-5 viable players.
"Walker? We could have taken him too, but we didn't have the money. But we couldn't take another non-EU player. I give the OK to whoever meets my needs. I'm the one who chooses for him."
He also said: "If you remember I said that the English say that Rome wasn't built in a day. I hope it doesn't take us ages, but give this ownership time to do what they have in mind.
"I also wanted Kolo Muani, then when we saw it we couldn't because of the salary. So what do we do? In Florence there's a saying that says 'It's easier to criticise than to do'. But we criticise the right thing and we know how to say things."