The Mirror reports that the Spanish giants are keen to bring in Agger to rejuvenate their defence.
Barcelona showed an interest in Agger last summer, but did not make a bid after the defender signed a new four-year contract with Liverpool.
The Catalans has earmarked Agger as a replacement for 34-year-old defender Carles Puyol at the Camp Nou.
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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.