Zimbabwean striker only found the back of the net three times this season but the Robers boss is keen to keep the former Manchester City man at Ewood Park
The striker joined Rovers at the start of the season on a one-year deal but failed to have the impact he would have liked as he struggled to score; registering only three goals in 21 appearances for the club.
However Kean has not ruled out extending the striker’s stay at the club for next season as he looks to rebuild his squad after a relegation threatened campaign.
"We are hopeful that we can put something together for Benjani," Kean told the Lancashire Telegraph.
"It will probably come on the FA website that he is a free transfer but we want him here.
“We haven't gone into detail with Benji but I said to him I would like to put something towards him and that will hopefully be done in the next couple of days.”
Benjani only started six times for Rovers as the club struggled to find a consistent line-up to fire them away from the relegation zone but Kean admitted he was happy with the contribution he received from the striker, despite his lack of goals, and hoped to have him involved with the squad for next season.
"He has done really well for us,” he continued. "The type of lad he is, he is happy to have a role as an impact player as a substitute or if he is in good form and has a run in the team, then I think he has shown he is a guy defenders don't want to play against.
"He certainly had a strong end to the season."