Scott and Kroupi have both been the subject of transfer speculation this summer, with reports linking the pair to a number of clubs, but Bournemouth's plan is understood to be to keep hold of both players, and Rose sounded confident he could do just that in his first season in charge.
Asked about the challenge of retaining his best players, Rose played down any sense of alarm.
"So far, it's not a challenge for me, to be honest," he said. "First four days we are in touch, and my feeling is that the boys feel really good here. And I know it from former clubs, it's always about timing."
Turning to Kroupi specifically, Rose added: "He's just 19. He did a great improvement last season, so I think for him there's no ceiling.
"But even he, I think, knows that he's here and on a good place to improve. He's playing Europe, he has many games, he's playing in the most competitive and intensive league in the world. So far I don't have the feeling that anyone tries to leave the club."
Scott's stock rose sharply last season after a string of consistent performances put him in contention for a potential World Cup call-up with England, a recognition that ultimately did not materialise but which underlined his emergence as one of the division's best young midfielders. He has two years remaining on his contract and has been offered a new deal this summer, though he is yet to make a decision.
"I started to speak with the players yesterday," Rose said, when asked specifically about keeping Scott. "I'm going to do it next days when we go for the training camp as a group, much more individual talks. And yeah, I think Alex knows what he has with this club. For me, it's always about the right moment to do the next step, because if you are a young player and you do steps too fast, too quick, you don't play, or you have another environment as a young player.
"If you leave your club, then it's getting difficult. And I think even the club here is doing a lot of things to show the players that they are in the right place. Improving things is always possible. My approach is close to the approach of Andoni, but even here we have some small things we're going to adapt. And I think with every new coach, the players get newer knowledge."