The former Liverpool manager was confirmed as the new Celtic boss last month.
Rodgers was confirmed as the new Celtic manager last month after Ronny Deila departed the club at the end of last season.
His arrival has been warmly welcomed at Paradise, with many believing they have pulled off a major coup in securing his signature.
There is hope that Rodgers can turn Celtic into a force in Europe once again after they have missed out on the Champions League in the last two seasons.
First and foremost however they must continue their domination of the Scottish Premiership, and Kennedy says that Rodgers is determined to dominate every game in Scotland.
“He wants to dominate every game in Scotland if we can and try to take that into Europe,” he told celticfc.net.
“He wants us to have no fear in the way we play and to turn Celtic Park into a real fortress. He wants to make sure teams know when they come to Celtic Park that they’ll be up against it and it’s important we do that.”
It will certainly be interesting to see what work that Rodgers can do at Celtic with expectations at a high.
His experience in the Premier League is likely to serve him well, but he will know that Scotland will not be a walkover in any regard.
Indeed, the former Liverpool boss arguably faces a much more difficult task than his predecessors, with Rangers' return making the competition for the title considerably tougher next season.