The Mirror says Kean is desperate to tie down exciting Canadian attacker Hoilett - whose dad has flown to England to help thrash out terms - before he gets into his current deal's final year.
The Rovers boss gave Hoilett his chance to shine and does not want to lose him, so is looking to give the home-grown kid a long-term deal on vastly improved terms.
Hoilett, a target for bigger clubs, is settled at Blackburn - the club he joined as a youth before being sent on loan to Germany until he qualified for a work-permit.
Rovers also want to sort out a new deal with French defender Givet.
He has been hit with a tax bill due to a misunderstanding over his last contract and Rovers owners Venky's are trying to sort out the problem.