Buffon left Parma for Juventus in 2001 and the 39-year-old has since gone on to become one of the greatest keepers of all-time, winning seven Scudetti among other trophies.
However, Italy's most-capped player almost moved to Camp Nou following an agreement with the LaLiga powerhouse.
"Yes, it was close," Martina told TuttoJuve as Juve prepare to face Barca in the quarter-finals of the Champions League, starting April 11.
"There was an agreement between Parma and Barcelona, but he picked Juventus."
Buffon is out of contract at the end of next season and the veteran shot-stopper has shown no signs of slowing down.
He could play beyond the 2018 World Cup in Russia but Martina said: "I don't know [if he will play until he is 40].
"He will decide when it should be when the time comes."
Buffon has been a mainstay for five-time defending champions Juve this season, playing 25 Serie A games and 33 in all competitions.