The 34-year-old is now free to sign with the club of his choice ... and will undoubtedly come with a massive price tag.

The team released a statement ... saying both sides agreed to make a deal, but due to "financial and structural obstacles (Spanish Liga regulations)," there was no way to make it happen.

"As a result of this situation, Messi shall not be staying on at FC Barcelona. Both parties deeply regret that the wishes of the player and the club will ultimately not be fulfilled."

Messi is one of the greatest soccer players ever -- he's won the Ballon d'Or a record 6 times -- and has spent his entire pro career with Barcelona.

The club added ... "FC Barcelona wholeheartedly expresses its gratitude to the player for his contribution to the aggrandisement of the club and wishes him all the very best for the future in his personal and professional life."

Messi was #2 on Forbes' highest-paid athletes list this year ... and in 2020, became the second player to ever have $1 billion in career earnings, behind Cristiano Ronaldo.