The Croatian striker, 23, lost out on starting opportunities since Kean took over last year and is now uncertain whether he will remain with the club.
Kalinic's agent confirmed to the Lancashire Telegraph that the situation would be resolved in the next ten days.
“We want to talk to the coach as soon as possible so we know what happens next," he said. "Nikola Kalinic is contracted to Blackburn and so we will not talk about other clubs.
“There are a lot of clubs we believe who would want Niko. He needs to know if he is going to play for Blackburn first though. There is no problem with the club and if they want him to stay he will stay.”
Kean previously outlined his intention to sign two new strikers this summer.