The legendary forward has asked to leave the La Liga side and hopes to exercise a clause in his contract which allows him to leave for free.
Barcelona feel that the clause has expired and that Messi has a contract until next year, with a 700 million Euro buy-out clause.
The 33-year-old made his debut at the club in 2004 and has since become their record goal scorer and won the Champions League four times.
Former Barcelona captain Carlos Puyol came out in support of Messi's decision, tweeting: "Respect and admiration, Leo. All my support, friend."
His team-mate Luis Suarez posted two clapping emojis in reaction to the news.
New Barcelona coach Ronald Koeman recently said that he hoped Messi would remain at the Nou Camp.
The Dutch manager said: "I don't know if I have to convince Messi [to stay]. Of course he is the best player in the world and you want the best player in the world in your team - you don't want him playing against you.
"For me as a coach, I would love to work with Messi because he wins matches. If he is at the ability and the level he has always shown, I would be more than happy for him to stay.
"He's still got a contract and he is still a Barcelona player. There are some older players in the team and we need to make some decisions but in Messi's case, I hope that he stays with us."