Fresh off of Barcelona’s embarrassing ouster from the Champions League earlier this month, Messi announced his intention in the bluntest way possible, the club confirmed, signaling that his frustration with the club had reached a breaking point. Though the stunning move doesn’t guarantee he will leave, Messi has put the world on notice for one of the wildest bidding wars in the history of sports.

Even at 33 years old, Messi is the highest-paid soccer player on the planet, earning a salary of more than $70 million a year, according to a Barcelona contract that was leaked in 2018. That kind of financial commitment is one that only a handful of clubs in the world could afford. If he is truly on the market, there is no question that they will take their once-in-a-lifetime shot.

Though Messi has never indicated a preference for where he might land after Barça, there are two obvious candidates—if only because they are the most lavish spenders in soccer.

Manchester City, owned by a member of Abu Dhabi’s royal family, could reunite him with the manager who shepherded Messi to the pinnacle of soccer at Barcelona from 2008 to 2012, Pep Guardiola. And Paris Saint-Germain, backed by an arm of Qatar’s sovereign-wealth fund, already has the two players who commanded the highest transfer fees in history on its books, Neymar and Kylian Mbappé.

Other suitors could emerge. Internazionale, in Milan, has undergone a rich rebuild under Chinese billionaire and Suning founder Zhang Jindong. Few things are beyond Chelsea or Manchester United either, as two of the richest sports teams in the sport happen to share Messi’s biggest sponsor, Adidas.

Before Messi can pose for a jarring photo shoot in another club’s jersey, there are technicalities to iron out around the conditions of his exit. Reports in Spain had suggested in recent weeks that Messi’s contract included a clause that allowed him to terminate his relationship with Barcelona unilaterally at the end of a season. The problem is that the clause may have expired during European soccer’s pandemic postponement.

There was also Messi’s buyout clause of €700 million ($828 million)—except it might not be enforceable if the contract expired in June, when the season normally would have ended. These are the questions that will occupy Barcelona’s lawyers over the coming days.

Meanwhile, as the club prepares to get bogged down in bargaining, some Barcelona fans are already moving on to acceptance.

“Catalonia will always be your home,” Quim Torra, the president of the Catalan government, wrote on Twitter Tuesday night. “Thank you so much for all this time of happiness and extraordinary football. We have been lucky enough to share a few years of our lives with the best player in the world.”

Barcelona is the only club Messi has ever known as a professional. He moved there as a shrimpy 13-year-old after coming from Argentina to join Barça’s legendary youth academy. At the age of 17, he cracked the first team and scored the first of his 634 goals for the club on his way to 33 major trophies in 16 years.

The team’s catastrophe in this season’s Champions League—Barcelona’s third in as many years—may have been the last straw for Messi, but tension had been building inside the club for months. He was known to disagree with club president Josep Maria Bartomeu about transfer policy. The boardroom was divided by political infighting. And Messi had personally fallen out with the club’s sporting director, Eric Abidal, after Abidal criticized “some players” for not working hard enough during Barça’s first trophyless campaign in 12 years.

It was enough for Messi, perhaps the quietest megastar in sports, to fire back.

“The players are responsible for what happens on the pitch, and we are also the first to acknowledge when we were not good,” Messi wrote in a rare Instagram outburst. “Those responsible for the area of sports management must also assume their responsibilities and above all take charge of the decisions they make…Finally, I think that when talking about players, we should give names because otherwise we are getting everyone dirty and feeding things that are said and are not true.”

The chaos flared up again after Barcelona lost the Spanish league to its bitter rival Real Madrid and crashed out of the Champions League to Bayern. Within days of the 8-2 loss, Abidal and manager Quique Setién were fired. Last week, the club hired Ronald Koeman to be its third coach in the space of 12 months.

“Respect and admiration, Leo,” tweeted former Barcelona captain Carles Puyol, a vocal critic of Barça’s current administration. “All my support, friend.”

Write to Joshua Robinson at joshua.robinson@wsj.com