Drinkwater joined the West London side in a £30m deal on the deadline day, and he could make his Blues debut at Leicester City on Saturday.
When asked if Drinkwater would fit in at his new club, Vardy said: “Will he fit in at Chelsea? It depends. They’re full of world-class players.
“Danny is up there himself but it depends on the formation their manager plays. They signed Tiemoue Bakayoko, so Danny has a lot of competition for his place.”