The attacking midfielder's current deal expires in the summer and Tottenham Hotspur are rumoured to be interested in the Canadian's services.
However, Kean believes that Rovers could be in a position to keep Hoilett if they can steer clear of relegation this season.
Kean told The Metro: "We hope we can get ourselves to a position of safety and make him an offer.
"We want him to stay here. He is playing out of his skin."
Blackburn are currently 16th in the Premier League.