The 29-year-old's future has been widely discussed with his contract expiring next year and talks seemingly progressing slowly.
But reports on Wednesday suggested Messi had agreed to a new deal until 2021 or 2022.
In an interview with Tencent Sports and published by ESPN, the Argentina star said he wanted to finish his career at Barca, the club he joined as a 13-year-old.
"It's what I always wanted and dreamed. I would love to finish my career at Barcelona," Messi said.
Messi has enjoyed a trophy-laden career at Camp Nou, winning eight La Liga titles and four Champions League crowns.
He has developed into arguably the world's greatest ever player, claiming the Ballon d'Or a record five times.