The 21-year-old has been linked with a move to Camp Nou recently and admits he would relish the prospect of a switch to a major league in the near future
The Spanish champions have been seeking a long-term successor to Victor Valdes for much of the campaign, with Borussia Monchengladbach's Marc-Andre ter Stegen and Pepe Reina of Liverpool two of the favourites to complete a move to Camp Nou this year to replace the outgoing Spaniard.
Fulli says he is proud to see his name linked with Barca in recent weeks as he aims to secure a switch to a major league in future.
"To have such a big team like Barca following you is rewarding," the 21-year-old told TV program Esports en Xarxa. "Barca have been the best team in the world in recent years.
"I'm very relaxed at Estudiantes, I want to do things right so that I could come to a great league in future."
Fulli went on to reveal his admiration for Barcelona star Lionel Messi, who scored a hat-trick in training in front of 12,000 fans after returning from a spell in his native Argentina where he was recovering from injury.
"There is no doubt that Messi is the best in the world," he said. "No-one else in the world can do what Messi does for Barcelona or Argentina. Barca must feel proud to have a player like him."
Fulli also praised the performance level of Valdes over recent seasons, but stressed Juventus keeper Gianluigi Buffon will go down as the finest in history.
"For me, the best goalkeeper is Buffon," he added. "He has been, and is going to be, the best ever. After him, there are huge keepers like Valdes. I watch him from a long way away and can't believe some of the things he saves."