Messi could walk away from the club as a free agent in two months' time, when his contract expires, but reports in Spain indicate Barcelona are making determined attempts to persuade him to stay.
New president Joan Laporta, back for a second spell at the helm, is reported to have recently had dinner with Jorge Messi, father of the 33-year-old whose record-breaking feats at Barcelona continue to beggar belief.
For a 12th successive season, Messi has scored at least 25 league goals, making him the only player in Europe's top five leagues to achieve the feat in consecutive campaigns this century.
Messi has reached that target this season despite doubts lingering over his future at Barca, after he requested a transfer during the last close season.
He has scored over 400 goals more than any other player in the club's history and this season has overtaken Xavi to set the record for most appearances.
Xavi, coach of Al Sadd in Qatar, has despaired at seeing his former team-mate disenchanted at times, telling TV3: "That he has not felt happy in what I consider to be the club of my life makes me sad, and something has had to be done very badly for Leo to not feel happy.
"You have to make sure that Leo is happy, because with a happy and content Leo you have more numbers to win titles. Many times I've had the impression that Leo has not been happy on the pitch, that he has been sad, and it makes me sad as a cule [Barcelona supporter] that we have not taken advantage of him enough in recent years.
"We had the best footballer in the world and in history and we haven't taken advantage of him enough."
According to TNT Sports, Paris Saint-Germain are preparing a blockbuster contract offer in an effort to draw Messi to the French capital.
While what Xavi says certainly held true for a significant stretch during Josep Maria Bartomeu's presidency, the return of Laporta appears to have lifted the mood around the club.
Captain Messi has appeared increasingly to be enjoying his football this season under coach Ronald Koeman's leadership, and his form in recent weeks has been dazzling.
Barca have won the Copa del Rey already and on Thursday have the chance to go top of LaLiga as they face Granada.