The Catalans won the Champions League, Copa del Rey and La Liga last term to become the first side ever to have lifted three major trophies in one season twice.
Barca first achieved the feat under Pep Guardiola back in 2009 and Busquets says the current squad are capable of doing it again in the coming years.
"The joy of winning is permanent, you cannot take it away," he told El Pais.
"All you want is more, more, more. And we have players of incredible quality, a super young team and a unique opportunity to extend this level of performances.
"In the Champions League final, if you take away Dani Alves, Javier Mascherano and Andres Iniesta, I don't think there was anyone over 30-years-old in our team.
"Marc-Andre Ter Stegen is super young and Neymar, Jordi Alba, and the rest - we are all between 23 and 28 years.
"We can win the treble every year, no one is invincible, but we have huge potential."
The 26-year-old also discussed in detail the evolution of Lionel Messi, who has operated in several different positions this season having played in a central role in previous years.
"Messi is improving every year and there have been tactical changes that have benefited the team and benefited him in recent years - he played false nine for a while and that caught our opponents by surprise and generated more surprise because there was more space.
"Now, after moving to the wing he makes the field huge. The diagonal passes from Alba, for example, are spectacular. He has been reinvented. Leo evolves and does so with the team. He is impossible to stop. He is the best."
Xavi's lifelong association with Barcelona came to an end after the season drew to a close, with the midfielder signing for Qatari side Al Sadd and Busquets admits life at Camp Nou won't be the same without him.
"I can't imagine the dressing room without Xavi, it's going to be weird. His presence is remarkable. He would arrive early and always say something to the group. We will feel his absence."