The Blaugrana coach also spoke about the recent acquisition of Neymar, Eric Abidal's imminent exit from Camp Nou and defended his decision to stay despite health issues
The Spain international, who has been a Blaugrana player his entire professional career, is 35 years old and has been ravaged by injury this season, triggering calls for Vilanova to plug the gap in his side's defense.
The coach has revealed that a center back will be one of Barca's targets in the upcoming transfer window but insisted he wants Puyol to recover from his injury and remain at Camp Nou regardless of his age.
"We'll be looking for a player in that position - in the middle of defense," he told reporters on Friday. "We hope Puyol recovers but we'll still be looking for a new player in that position. He's said he wants to play until he's 40 and I hope he does!"
Two players who have been linked with a move away from the club are David Villa and Thiago, but Vilanova has stressed that no decision has been made about the pair.
"We haven't talked about whether Villa's going to leave the club," he added. "As for his performance over the last three years, he's been very good. It's been a pity about the serious injury he had [in December 2011]. He has a good relationship with the fans, he scored a goal in the Champions League final.
"I don't know anything about Thiago wanting to leave. Thiago has a future here at Barcelona. We want him to stay but it depends on him. There's a lot of competition in midfield. It's up to the player if he wants to continue but it's not only us having confidence in him, but him having confidence in himself."
The first player who has been confirmed as leaving is defender Eric Abidal - Vilanova admitted that the club's decision was hard, but hopes he can find success away from the Liga champions.
"I feel bad that Eric Abidal won't stay on, but it's a decision the club has taken," he said. "We won't find another player like Abidal. The decision was very difficult. I hope he finds a good club and proves us wrong."
Barca made its first signing of the summer in the past week by signing up Santos starlet Neymar, beating Real Madrid to his signature, and Vilanova had plenty of praise for his new forward.
"Well I think Neymar's a player who can play in many positions, not only on the left," he said, when asked where he would play the 21-year-old.
"He's a really top player, he combines well with other players. He's good defensively and tactically he's going to help us as well. Every club in Europe wanted to get him but we're convinced that he's a player who can score goals for us."
Vilanova swatted aside rumors that he will quit and brushed off comments from Barca legend Johan Cruyff that he should step down to concentrate on recovering from cancer.
"I can't make it any clearer, I can't say it any louder - I'm staying at Barcelona," he insisted. "People talk about things - Mr Cruyff talked about my health and the club. When he makes these kind of declarations then people listen."
Barca faces Malaga on Saturday in what will be its final game of a successful Liga season, though star attacker Lionel Messi - who was called up to Argentina's squad for matches in June - remains sidelined with a hamstring injury and will not feature according to the coach.
Vilanova said: "No, Messi won't be playing tomorrow. He doesn't have the green light from the doctors.
"If he can play for Argentina then he will get to play, but obviously we don't want to take any risks with him. We don't want him to get injured again."