The captain has committed his future to Rovers until the summer of 2023, despite strong interest from other clubs.
And he says 'one of a kind' Moore was the primary reason he was so keen to remain at the Keepmoat.
"In terms of the way he treats every day, the way he treats people, the way he treats football in general, he's incredible," Whiteman said.
"He loves the game, as I do. We have conversations about the games - not just in our league but in others as well.
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"I like learning in the day. For example in training I like knowing what we're doing each day and why we're doing it.
"How in depth he does things, with movement off the ball and things like that - he's just a proper football person.
"I can't really think of anyone like him in football, especially in our country at the minute, who has got that full package – someone who is a very humble man and he loves the game as much as he does, plus how he treats other people.”
Moore has proved overwhelmingly popular with the Rovers squad since he took charge of the club in the summer, with players eager to sing his praises.
And Whiteman revealed the deep affection for the manager has a knock-on effect when results do not go well.
He said: “In a way, and I know it sounds daft, but you feel when you lose that you've let him down. It's a horrible feeling.
“In your first meeting, the sheer size of him, you suddenly think you respect him anyway.
“It's not just that, it's the different sides he has got to him.
“The staff he's brought in as well – Jamie Smith has been different class.
“I can't really explain what it is that he's got. You just want to work hard for him and win for him.
“He's the perfect fit for the football club.”