The Atletico Madrid forward has been heavily linked to the Catalans with a summer transfer seemingly in the works.
“I made the decision to go to the best club in the world but it took a lot of time for me to leave Valencia, where I was very comfortable,” the left-back recounted of his own transfer to the Camp Nou.
“I suppose he will have the same feelings, but any player wants to progress.”
Griezmann scored a brace as Atletico beat Marsielle to lift the Europa League last week and Alba is certain the Frenchman will boost an already potent Barca attack.
“He is a player who links well, who has an eye for goal and can play in several attacking positions.
“He would be a good signing for Barcelona.”