The 22-year-old has been strongly linked with a move away following Rovers' relegation, but the Scot is hoping to hold onto his best players ahead of a promotion push
The Canadian is without a club after leaving Ewood Park and has been strongly linked to joining both Tottenham and Borussia Monchengladbach.
However, Kean remains hopeful that Hoilett could return ahead of Rovers' push for promotion to the Premier League.
"Junior is out of contract and we've made him a very good offer. It's not dead yet," Kean told BBC Radio Lancashire.
"If a club in this country signs him, there will be big compensation. We'd like him still to be here but I'm in the dark a little bit.
"When a player runs out of contract, you make him a good offer and he doesn't sign, you fear the worst, but we'll just have to wait and see."
Hoilett bagged seven goals in 37 appearances for Blackburn last season, and was one of the club's standout performers, despite their eventual relegation.