Palmer has scored 48 goals for Chelsea in all competitions since joining the club in 2023 and was key to last year's Club World Cup-winning campaign.
However, his game time has been restricted this season due to a persistent groin injury and a broken toe, with British media reporting this week that the 23-year-old was unsettled and open to a move.
"I've had numerous conversations with Cole, and he seems very, very happy to be here," Rosenior told reporters ahead of a trip to Crystal Palace on Sunday.
"He's a huge part of our plans in the long term. He's an outstanding player. Every player goes through difficult moments in their careers in terms of injury. I don't think it's any reflection on his qualities.
"He's an outstanding footballer. But my job and the club's job is to get him in a place where he can consistently perform at the level that he wants to."
Palmer scored from the penalty spot in Chelsea's 2-0 league win over Brentford on Saturday, but his celebrations were muted as he cut a frustrated figure.
He then missed Chelsea's 1-0 win over Cypriot side Pafos in the Champions League on Wednesday.
"He was in pain. He couldn't perform to the level he wanted to do for the club. He's a great kid, and he's an outstanding player," Rosenior said.
"But we have to make sure that we look after him in the right way. That's why I haven't involved him in the last game... Cole's in a good place. He's joined training today, which is really positive, and we'll assess his reaction to training."
Chelsea, sixth in the standings, next take on a Palace side who have fallen to 13th after a seven-game winless run.
Palace have also lost defender Marc Guehi, their former captain, to Manchester City and their manager Oliver Glasner announced last week that he would leave the club at the end of the season.
Asked if it was a good time to face them, Rosenior said: "I think it can be reported in that way. What I do know is they're an outstanding team. Selhurst Park is, for me, one of the most difficult places to go in the Premier League.
"You have to be ready for a physical battle. The atmosphere in the stadium is going to be red-hot. So we're not taking the game lightly at all."