Barca president Joan Laporta told ESPN last week that he considers it his responsibility to ensure Messi has a "more beautiful ending" at Camp Nou following his painful exit last summer.
However, Xavi has played down the chances of re-signing Messi from Paris Saint-Germain, who he joined on a two-year contract last summer because Barca could not afford to renew his deal.
"Leo has a contract, so it's impossible, impossible," Xavi told a news conference in Dallas ahead of Tuesday's friendly against Juventus at the Cotton Bowl.
"It doesn't make sense to speak about Messi. He is the best player in the world and the best ever. The president has already said that he hopes Messi's story has not finished with Barcelona. We will see in the future, but it's not the moment to speak about Leo, it's the moment to talk about the exciting players we have here."
The post-Messi era has cranked up a gear at Barcelona this summer with the signings of attackers Robert Lewandowski and Raphinha. They follow the January arrivals of Ferran Torres and Pierre-Emerick Aubameyang.
Messi will be 36 when his contract expires with PSG in 2023, but reports continue to link him with a Barca return. Following Laporta's comments to ESPN, Diario Sport reported that Xavi had asked the president to try to sign him on a free transfer next summer.
Messi's departure from the Catalan club left a bitter taste. He was prepared to accept a lower salary to stay, but Barca were still unable to fit his wages within their LaLiga-imposed spending limit.
"Messi was everything," Laporta said exclusively to ESPN last week.
"To Barca, he's been possibly [the club's] greatest player, the most efficient. To me, he's only comparable to Johan Cruyff. But it had to happen one day. We had to make a decision as a consequence of what we inherited.
"I would hope that the Messi chapter isn't over. I think it's our responsibility to try to ... find a moment to fix that chapter, which is still open and hasn't closed, so it turns out as it should have, and that it has a more beautiful ending.
"As president of Barca, I did what I had to do. But also, as president of Barca, and on a personal level, I think I owe him."
Laporta has previously spoken of his desire to see Messi back at Barca, where he won the Ballon d'Or on six occasions, as well as holding the club's records for goals (672) and appearances (778).