The newly promoted Ligue 1 club have already signed Joao Moutinho and James Rodriguez, with Radamel Falcao set to follow.
Carvalho was allowed to leave Real Madrid, whom he has been with since playing for Chelsea.
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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.