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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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.