The Brazilian star has been exceptional for the Red Devils since his arrival from Real Madrid last summer.
Casemiro fitted seamlessly into Erik ten Hag's team and appears to love life at Old Trafford under the Dutchman.
The 31-year-old has seen the club sign Mason Mount and Andre Onana this summer as a rebuild ahead of their Champions League return continues.
But Man United still need a new centre-forward with Atalanta star Rasmus Hojlund the main transfer target.
And Casemiro is keen for progression to continue ahead of the new campaign.
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"I think we're growing, I think we are evolving, right?" said Casemiro. "I think that always, when anyone speaks about Manchester United, the club is about winning
"The club always aspires to win things, but we know that we're growing, that we're embracing the ideas of the coach and I think we're on the right path. What I want is that the club is in a good way, that the club is as high as possible.
"We won a trophy last year, we finished third and we played in another final. We have to continue evolving, because when we talk about individuals, it's a little bit hard, because this is a team game. It's a team with 11 and the key to winning a trophy is to have a good team with those players who come in."
But despite the evolution, the Brazilian has counselled caution about setting expectations too high.
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"I think it's too early to talk about the Champions League," said Casemiro.
"We're in pre-season still and we're growing. No one likes to lose a game like we did, but these games are about getting rhythm, the sensations you have, working hard, fighting and keeping on growing as a team."