Rovers are currently on a mid-season tour of India and secured a 3-0 win over 10-man Pune FC in an exhibition match on Friday with a brace from Jason Roberts and one from Ruben Rochina.
Under Kean, Rovers have taken just four points from their opening seven Premier League games this term, and the frustration of the fans has been evident during this tour of the sub-continent.
The Venky family, who own the club, are refusing to abandon Kean and believe that he will eventually steer the club in the right direction.
Co-owner Balaji Rao told the Daily Mirror: "The team is in the relegation zone now but it's going to come up, I am sure of that.
"We do know a few people have been generating thousands of emails demanding the ousting of Steve Kean, who is a brilliant manager.
"But we know the team is going in the right direction and we are very positive about the way the team is performing and the way it is going."
The claims of Rao are likely to further rile the Rovers faithful, with the club currently sitting second from bottom in the standings.
But their owner has a five-year plan to see them secure a place in Europe.
"On the whole, the goal of playing in Europe in the next four or five years is a realistic one," he added.