Rovers have rejected two offers from Rangers for the centre-back but have not yet received enquiries from either Tottenham or Paris Saint-Germain, who have both been linked with Samba.
The 27-year-old this week handed in a transfer request but he is under contract at Ewood Park until 2015 and the club on Tuesday reiterated their stance that he is not for sale.
Kean told Sky Sports News: "The statement reads for itself. We want to keep Chris. Obviously we know there's bids out there for him but it's a mark of what we're trying to do that we've refused the bids and that's where we are.
"We've only had two bids from one club. There's not been any other clubs in contact. Chris is under contract and we've been in dialogue with Chris yesterday. We want him to stay at the club and that's what we'll be fighting to do."
Samba missed last weekend's win over Fulham, which helped Blackburn climb out of the Premier League relegation zone, with illness but should be back in training on Thursday and could feature in Saturday's trip to Everton.
Kean, meanwhile, gave short shrift to newspaper reports on Wednesday that, were Samba to leave, his defensive partner Scott Dann would also seek a move away from Rovers.
"I've dismissed that totally that there was anything in Scott's contract that said Chris had to stay," Kean said.
The Scot has so far been unable to add to his squad this month but moved to reassure fans that the club is working hard to ensure there will be new arrivals.
Kean said: "I think it's been quite slow for a number of clubs and we're one of them. We've been very active; myself, the directors, the owners. We've had extensive lists, we've got bids and we're hopeful we can bring new faces in."
Rovers could return with a higher bid for Fulham striker Andrew Johnson, and Kean added: "We respect Fulham and we don't want to disclose what level that's at. That's one name but there's another four or five names we're actively trying to pursue."
There is expected to be one new face at Blackburn this week, though, with Kean close to naming his new assistant manager following the departure of Paul Clement, who joined Paris Saint-Germain earlier this month.
"We had good talks last week with a number of very good candidates and we're very confident we can announce something tomorrow," Kean said.
