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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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.