The Burnley forward has had limited opportunities this season, and has yet to score a Premier League goal with his last two appearances coming off the bench.
Kane has eight goals for Tottenham already this season, and earned the praise of his countryman.
“I feel he is (the best in the country),” said Rodriguez, who was once linked with the England squad.
“I feel like he’s got everything as a striker. As a character, as a person obviously I don’t know him but what you see of him is level-headed but also ruthless in everything he does on the pitch.
“He can finish any type of finish and he’s world class and I think definitely the best striker.
“So it’s always good to go against these types of players and it’s good to say that.”
The Clarets are still without a victory in the Premier League after nine matches and have dropped 11 points from winning positions this season.
The goals have been more forthcoming in the cup with a 4-1 win over Rochdale in the previous round, in which Rodriguez scored all four in the second half.
Although Burnley needed penalties to beat Newcastle in the second round after a goalless stalemate, Rodriguez believes victory against Tottenham could kickstart a run of form for the Clarets.
“Definitely, a game is a game. To get that winning mentality you need to win so for us if you do go and win it’s definitely going to go into the next game,” the Burnley forward said.
“We’re not far from it, we’ve had some great performances just have been unlucky enough not to win but I’m sure that win is definitely around the corner, hopefully.
“Every time we step out onto the pitch we’re aiming to win and as soon as that first win comes, hopefully there will be many more to come.”