The People reports that the Spaniards are ready to make a move for Coutinho, if they qualify for the knockout stages of the Champions League.
Atletico Madrid made their interest in Coutinho known in the summer, but that was quickly rebuffed by Liverpool.
But the Spanish side could make an bid for the 21-year-old in the January transfer window.
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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.