Suarez's performances over the last couple of seasons have made him one of the most sought-after forwards in European football, with Barcelona strongly linked with a move.
Thus far Liverpool have repelled the interest, but according to Gabri, who played with Suarez at Ajax, the 27-year-old wants to move to Spain.
"He's a player that has always considered coming here one day, and if he did it would make me very happy," he told La Xarxa.
"I think Barca would be making a great signing. He would adapt very quickly because of his hunger and he would be a very good fit for the club. He also has his wife's family in Barcelona.
"He's mature as a footballer. He's a player with character and personality. If he were to come to Barcelona he would have what it takes to deal with the pressure of playing for a club like Barca."
Suarez signed a new long-term deal with Liverpool last year.