Rovers suffered their first home defeat of the Championship season in a 2-1 loss to Middlesbrough on Friday, prompting speculation that the club's owners were negotiating Kean's replacement as manager.
The owners' talks are expected to continue, but operations director Paul Agnew has said the club will not be responding to media speculation at this time.
Kean replaced Sam Allardyce as manager in December 2010 and has faced almost constant criticism since. The club avoided relegation on the final day of the 2010-11 season but went down last year.
They are second in the Championship table after seven matches. There were widespread calls for his sacking from the terraces in the come-from-behind win over Barnsley last week, and then even more vociferous abuse during the match against Boro.
After the game he told the BBC: "I'm disappointed [with the defeat] but we're in a position where we are, on average, picking up two points per game.
"If we can do that for the whole season, that will see us getting promoted and that's the one goal we've got."