O Jogo claims the La Liga giants would pay 90&% of his salary.
Real Madrid have been mentioned in connection with a potential world-record bid for dazzling playmaker.
The 27-year-old said of his United future: 'I want to keep improving to continue winning things.'
Catalans are said to be in talks to complete £43.7m signing.
Former Athletic Bilbao boss was presented as new Barcelona manager on 1 June.
Manchester United, Chelsea and Inter Milan have been linked with the Colombian international in recent times.
The Spanish side's attempts to overturn a ban were rejected by CAS on Thursday.
Agent Rodrigo Fernandez Lovelle confirms that Gunners have been informed of Perez's desire to leave.
Former Sevilla full-back says he is "100% staying" at the Nou Camp next season.
Unal has successfully completed his medical and will sign a five-year deal at Villarreal.
De Gea has two years remaining on his current contract with United.
France international says his agents are currently in talks with club officials over his future.
Under 21 Spanish international has spent the 2016-2017 season on loan at White Hart Lane.
Carevic, 18, has been a regular for OFK Grbalj for the last two seasons.
Italy international sees himself still playing in the French capital next season.
Turkish international has been linked with Arsenal in recent times.
The Spain international has stressed that no player is bigger than Atletico.
Iniesta, 33, has 12 months left on his contract at Camp Nou.
39-year-old should be ready to start at the Millennium Stadium on Saturday night.
53-year-old has signed a two-year deal with the option of a third to replace Luis Enrique.
Incoming Barcelona boss Ernesto Valverde is keen to bring the midfielder to the Nou Camp.
Rakuten appears on the front of the shirt for the first time after replacing Qatar Airways.