Despite agreeing a new five-year contract at the club only five months ago, the Congolese defender has been heavily linked with a departure from Ewood Park.
North London duo Arsenal and Tottenham Hotspur are both said to be among the parties interested in the defender's signature.
But Kean is determined to cling on to the 27-year-old, having already lost Phil Jones to Manchester United earlier this summer.
And he hopes his efforts to keep Samba at the club will see the defender reject the reported interest from other Premier League sides.
"We're trying to keep Chris and the fact that he's a couple of months into a new five-year contract shows the commitment we have shown to Chris,” the Scot said in The Mirror.
"The owners backed the proposal that I put in front of them to say 'let's get Chris a new contract and show what we feel about Chris'. There have been no bids at all for Chris at this stage."
Samba arrived at Ewood Park from German side Hertha Berlin in a deal worth £450,000 in January 2007, and has since gone on to become one of the most highly regarded defenders in the Premier League.
By Josh Robbins
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