Rossi, a free agent, is currently training with former club Manchester United.
"Barça wanted me when Pep Guardiola was there," the 32-year-old told AS.
"Football's like that though. I didn't go, I stayed at Villarreal and now it's history. It's a nice story because [Barça] are the biggest club in the world. It was an honour to be close to joining Barça."