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The 32-year-old Brazilian midfielder arrived at the Camp Nou after his £36.4m acquisition from Guangzhou in 2017.
Paulinho enjoyed a successful season with Barcelona as he scored nine times and registered three assists in 49 appearances.
And the former Barcelona star lifted the La Liga title and Copa del Rey before he re-signed for Guangzhou in 2018 on a loan deal, which was later made permanent in 2019.
Paulinho's second spell at the Chinese club came to an end on Sunday after his contract was mutually terminated due to the coronavirus pandemic.
The ex-Guangzhou and Tottenham player has now insisted that Barcelona "would not have to pay a transfer fee for me" if they approached him this summer.
Paulinho added that the issue of money or contract duration would mean "even less if Barca are the team who calls."
Speaking to Mundo Deportivo, he said: "For me, the theme of money or the duration of the contract would be a problem, they never have been, and even less if Barca are the team who calls.
"I have already shown when I left Guangzhou to go there for much less of what is perceived in China.
"Money has never been at the front in my career, so it would not be a problem in returning there. Also, the club would not have to pay a transfer fee for me."
Barcelona have been active in the transfer window and already secured Sergio Aguero, Eric Garcia and Memphis Depay on a free.
Paulinho's return on a free transfer would bolster Ronald Koeman's midfield options, as Barcelona challenge Atletico Madrid and Real Madrid for the La Liga title next season.
Guangzhou confirmed that Paulinho would be unable to fulfil his contract obligations due to travel restrictions amid the COVID-19 pandemic.
"Due to the COVID-19 pandemic and travel restrictions, Paulinho has been unable to join up with the club and perform the contract," the club's statement reads.
"After a friendly consultation, the club and the player decided to terminate the contract."
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