The 35-year-old Argentina forward is Barcelona’s all-time top scorer with 672 goals in 778 games and left the Nou Camp for financial reasons in 2021.
“Leo and his family know the affection I have for them,” Yuste said.
Messi agreed a new deal with Barcelona on reduced wages two years ago, but it was dependent on the club selling players following new financial rules.
That did not happen in time and ended his storied spell at the club which yielded four Champions Leagues and 10 La Liga titles – plus six Ballons d’Or.
“I participated in the negotiations which unfortunately did not lead to a certain result,” said Yuste.
“I’ve always had this thorn in my side that Leo couldn’t continue at our club.
“Messi knows how much we appreciate him. I would love for him to come back. We’re in contact, of course, with them.”
Messi, who won the World Cup with Argentina in December, has scored 29 goals in 66 games for PSG.
He recently claimed his 100th international goal and 800th career strike.