Samba handed in a transfer request this week but Kean said the club are determined that Samba honours his contract.
The Congo defender will be allowed to keep the captaincy if he proves his commitment to the club, added the Rovers manager.
Kean said on Thursday: "I spoke with him yesterday and he knows he is not for sale. The day before he handed in a transfer request, that has been refused and we won't welcome any more bids and Chris knows the stance of the club.
"It is never nice when somebody hands in a transfer request but hopefully we can now move on."
Kean said he had the 100% backing of Blackburn's owners Venky's but accepted Samba might need time to accept the decision.
Asked if Samba would retain the captaincy, Kean said: "If he's playing and performing well and still wants to be at the club, yes."
Kean confirmed an agreement was close for Eric Black to be appointed as the new assistant manager and that French striker Anthony Modeste is having a medical ahead of a six-month loan deal from Bordeaux.
