Acheampong started both matches since Rosenior took charge, featuring at right-back against Charlton and Arsenal. The 19-year-old Chelsea Academy graduate caught the eye with his calm defending, tidy use of the ball and confidence to support attacks.
Rosenior said the early signs from Acheampong, both on and off the pitch, had been extremely positive.
"I've been so impressed with Josh so far in the last two games and in training," Rosenior said. "He's a very level-headed kid with a lot of humility, which is a great sign."
The Chelsea head coach highlighted Acheampong's versatility as a major strength, especially for such a young player.
"The beautiful thing with Josh is that he can play five different positions," Rosenior explained. "He can play on the left, he can play centre-back, he can play right centre-back, he can play midfield, he can play on the wing. That's a great thing to have for a player of his age and temperament.
"I'm going to keep pushing him and I'm going to keep demanding different things from him because he has a really, really bright future."
Chelsea's next test comes on Saturday when they host Brentford at Stamford Bridge in the Premier League, giving Acheampong another chance to stake his claim.
Rosenior also stressed the importance of experienced players guiding younger members of the squad. He pointed to Reece James, another Academy graduate with experience across similar positions, as a valuable influence on Acheampong.
"When I was a player, the most important conversations I had were with senior players," Rosenior said. "If it's Josh speaking to Reece James, that is an unbelievable conversation with the experiences Reece has had.
"I want to encourage that interaction between the group, but I also want the players to feel confident enough in their own game and abilities."
With his versatility, attitude and willingness to learn, Acheampong appears well placed to continue his development as Rosenior looks to shape Chelsea's future.
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