Luiz would cost Barcelona in the region of €40 million, whilst Agger would be the second option and slightly cheaper.
Mundo Deportivo report that the Spanish giants are negotiating with Liverpool and Chelsea over the sale of the players.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.