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 start of the 2017-18 Premier League season is just around the corner and is shaping up to be one of the most competitive yet.
As always it is the so called “big clubs” that have splashed the most cash in the transfer window so far this summer. Manchester United or City? Arsenal or Tottenham? Who are the winners and losers of the transfer window so far?