The Foxes, still second in the table after defeats for Watford and Crystal Palace this week, can start to eat into the Bluebirds' 10-point lead when they host struggling Wolves on Thursday night.
Victory for Leicester at the King Power Stadium would put the pressure on their rivals ahead of their matches at the weekend, and Drinkwater told Press Association Sport: "It's massively important that we do that.
"We've got ourselves into a good position and we need to stay there. If we can get another three points on Thursday night then it could be massive.
"It would move us closer to Cardiff and put a bit of breathing space between us and the other sides in the chasing pack. Then we can enjoy the weekend off and watch how everyone else gets on.
"I can't see why we can't catch Cardiff. There are still 18 games to go and we've still got them to play. It is a weird league and anything can happen."
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