Messi's contract with Paris Saint Germain expires this summer and they are yet to agree an extension.
The 35-year-old Argentina international ended a 21-year association with Barcelona in the summer of 2021 when he joined Paris Saint Germain on a free transfer after the Catalan giants failed to put a suitable financial package together to retain the seven-time Ballon d’or winner.
Messi made 778 appearances for Barcelona after making his debut in 2003 and is the club’s all-time top scorer with 672 goals. He won 35 trophies with the club including four UEFA Champions League trophies and 10 La Liga titles.
Messi has also been linked with a move to America's Major League Soccer but Yuste has not ruled out a reunion with their former captain.
"Of course we are in contact with Messi," Yuste said on Friday. "Leo and his family know the affection I have for him, that we have them.
"I participated in the negotiations that did not come to fruition two years ago. I have that thorn stuck in me, and if we talk about La Masia, we talk about Leo.
"I would love for him to come back and I think the fans would too, because beautiful stories in life have to have a happy ending.
"We are in love with Messi and I think Messi is in love with Barca and the city of Barcelona."
