The duo have recently been linked with moves away from the Catalan club, albeit for different reasons, with Valdes refusing to confirm whether he will extend his contract beyond 2014 and Villa struggling to hold down a regular first-team place.
Neither player's future is giving Rosell too much trouble, however, and he is confident Valdes in particular will remain at the Nou Camp for a long time to come.
"I don't think it's true that he has decided not to renew. I think he will be another of the homegrown batch who will end his career at the club," said Rosell speaking to RAC1 and quoted in Marca.
"That's what I believe and that's my dream but I know he has to share the dream. I'm not looking for any alternatives."
Villa has struggled to retain a place in Barca's starting XI since breaking his leg in a Club World Cup match in December 2011, an injury that left him on the sidelines for eight months.
"Villa will not leave. But coming back from a serious injury to play in this team is not easy," added Rosell.
The rumours of Villa's departure have not been helped by Barca's continual link with Santos' much sought-after striker Neymar. However, Rosell said: "He has a contract until 2014 and then we'll see. It's not clear-cut that he would come to Barca."
Barcelona's president was also keen to pay tribute to Lionel Messi, who continues to inspire Tito Vilanova's side.
The Argentinian celebrated winning his fourth consecutive Ballon d'Or award last week by scoring in his ninth consecutive Primera Division game and playing a hand in the two other goals in Barca's 3-1 win at Malaga on Sunday.
"It's not hard to manage talent, only personalities. His talent will be written through the history of football and he has a personality that's easy to manage," said Rosell. "And I don't think he's even the best-paid player in the world."