Although domestically the Catalans continue to be a force, they have not been able to win the Champions League or even reach a final since they lifted the trophy in Berlin in 2015.
Barcelona suffered painful eliminations by Juventus, Roma, Liverpool and most recently by Bayern Munich, in a humiliating 8-2 thrashing, which has led Messi to say enough is enough.
The forward, 33, wants to be part of a sporting project which can help him see out his career in a blaze of glory.
FRONT RUNNERS
There are three clubs in front of the pack: Manchester City, Inter Milan and Paris Saint-Germain.
The English side have offered Messi a tempting deal according to reports, which could see him later play for franchise New York City after three seasons in the Premier League, and then go on to an ambassadorial role.
City's manager is Pep Guardiola, coach when Messi won the treble with at Barcelona among a trophy-laden spell, while his close friend and Argentina team-mate Sergio Aguero also plays for the club.
Ferran Soriano, the former Barcelona executive, is in charge of negotiations and he too has a good relationship with Messi.
Serie A side Inter Milan, meanwhile, have long courted Messi’s signature and are on good terms with the player’s family.
Messi’s father, Jorge, recently bought a house in Milan, which is being taken in some quarters as a sign of laying down the groundwork for the player to move to Italy.
Inter’s owners, the China's Suning Group, are said to be desperate to sign the Argentine star and have the financial muscle to do so, especially now the club has returned to the Champions League.
Perhaps most importantly, the tax laws in Italy would allow Messi to keep a lot more of his earnings, which is one reason other big stars like his former Real Madrid rival Cristiano Ronaldo, have moved there.
Paris Saint-Germain, meanwhile, reached this season’s Champions League final, where they finished runners up to Bayern Munich in a tight match, far closer than Barcelona’s historic capitulation.
Messi’s friend Neymar plays there and alongside the Brazilian and the next big star, Kylian Mbappe, he could help form an unstoppable attack.
OTHER ELITE OPTIONS
Other elite sides who might be able to put together a package to lure Messi include Real Madrid, Bayern and Manchester United. 
That trio have the financial muscle, but other factors may stop the move happening.
Messi moving to Madrid would be the most controversial move in football history, surpassing even that of Luis Figo, who made the same switch in 2000.
Messi is unlikely to rate Manchester United’s project compared with that of neighbours City, while Guardiola against Ole Gunnar Solskjaer is not a battle the Norwegian manager is going to win.
Bayern, meanwhile, are unlikely to rip apart the best side in European club football to try and find a home for Messi, at his age.
NOWHERE
There is a chance that Messi is trying to pull the strings of power at Camp Nou and force president Josep Maria Bartomeu and his board to resign.
They are perceived to be at fault for the club’s lack of success in recent years on the European stage, having spent over 300 million euros (355 million dollars) on signings like Philippe Coutinho, Ousmane Dembele and Antoine Griezmann, who flopped or underachieved with Barcelona.
Perhaps Messi's request is a bid to force early elections at Camp Nou and start the change which patently needs to happen in the club offices, although indications are Bartomeu has no intention of stepping down.
STEP BACK
If none of the offers appeal to Messi, he may instead look for a move to a more lucrative, lower-pressure division. MLS football in the United States might appeal, or he could follow former team-mates Andres Iniesta to Japan or Xavi Hernandez to Qatar.