“Leicester won't finish in the C Lge places,” Keys wrote on his website. “They’ll do well to finish in one of the European places, but I'm going to enjoy watching them try.
“I hope they do by the way. They'd deserve it, but they'll have to hang on to Vardy in January to get anywhere near.”
Leicester are third in the Premier League table at the moment with 22 points from 11 matches, just three points behind leaders Manchester City.
At the start of the season, many would have expected the Foxes to be fighting for survival in the English top flight, but they could end up in a European place.
Vardy has been one of the best players for Leicester so far this season and is in superb form at the moment.
The England international striker has scored as many as 11 goals so far this campaign and is only the third player to have found the target in eight back-to-back Premier League matches.
Leicester will face Watford at the King Power Stadium in the Premier League on Saturday.