Aguero is out of contract at the end of the season and with no new deal in sight, his future at the Etihad is in doubt.
Spanish outlet Cadena SER reports that Aguero said he would happily head to Catalonia when his representatives were approached about a possible free transfer.
Two candidates for next month’s Barcelona presidential election, Victor Font and Joan Laporta, are said to have looked into signing the 32-year-old.
The fact that the Argentina international would be available on a free is significant, given the financial problems facing Barca amid the coronavirus pandemic.
But Aguero’s arrival could also prove to be important as a way of convincing his friend and compatriot Lionel Messi to stay put.
The striker’s season has been disrupted by injury and a recent positive coronavirus test, and he is yet to score a Premier League goal in five appearances.
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