Former first-team coach Kean was appointed as the successor to Sam Allardyce in December despite no previous managerial experience and signed a two-and-a-half-year contract the following month.
Staying put: Blackburn's owners insist under-fire manager Steve Kean will remain in charge
Early results, which included a victory over Liverpool, were encouraging but Saturday's 3-2 loss to Fulham continued a worrying run that has left them only two points above the relegation zone.
But Blackburn co-owner Venkatesh Rao gave his backing to Kean, telling Sky Sports News: 'He is very much there, he has just signed a contract and we like him a lot, he is very enthusiastic and he is very positive.'
Rao conceded the owners are worried by recent results but is optimistic the club are on the right track.
He added: 'Yes, we are very concerned but we are now trying to improve all aspects. Plans are looking very positive and I am sure in the future we will do something better.'
Spot of bother: Blackburn went down 3-2 to Fulham at Craven Cottage at the weekend
Venky's issued an official statement via the club's website with chairman Anuradha Desai saying: 'I do not know the source of these rumours but I would like to clarify that there is absolutely no truth in these reports.
'I would like to put on record that we have a contract with Steve Kean and he will continue in his present position with the club.
'There is no question of the manager being changed.'
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