The Argentine's request to leave Barca comes a day after Spanish media reported that new coach Ronald Koeman told Messi's close friend and strike partner, Luis Suarez, that he does not wish the Uruguayan to stay at the club.
Other reports said that Chilean midfielder Arturo Vidal, Croatian midfielder Ivan Rakitic and French defender Samuel Umtiti have also been told they are no longer wanted.
Barca are in the midst of overhauling their squad following the 8-2 defeat by Bayern in the Champions League quarter-finals earlier this month, which condemned the club to a trophyless season for the first time in 12 years.
Messi, who has been named world player of the year a record six times, has grown increasingly unhappy in the last 12 months with how the club is being run under president Josep Maria Bartomeu.
In February, he lashed out at then sporting director Eric Abidal on social media and a couple of months later turned his anger on the club hierarchy for the way in which players were forced to take a pay cut to cope with the financial hit of the coronanvirus pandemic.
After Barca surrendered the La Liga title to Real Madrid in July, Messi slammed the team as being weak and vulnerable during an uncharacteristically fiery post-match interview.
Former Barca captain Carles Puyol backed Messi's wish to leave the club by writing on Twitter: Respect and admiration, Leo. You have all my support, friend.
Suarez then replied to Carlos' tweet with two clapping emojis.
Ex-Barca president Joan Laporta blamed Bartomeu for the stance taken by Messi.
Bartomeu and his board should quit immediately. They have undermined Messi to save them from the sporting and financial mess they have created. If they quit there might be some hope that Messi stays at Barca, he tweeted.
Catalonia's regional leader Quim Torra appeared to accept that Barca's best ever player, who in 2019 was given the Creu de Sant Jordi award for services to the region, was about to leave.
He tweeted: Catalonia will always be your home. Many thanks for all the happy moments and for your extraordinary football. We have been so lucky to share so many years of our lives with the best player in the world and a noble sportsman.