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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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.