The Portuguese midfielder has been strongly linked with a move to the Premier League in the past but no deal has materialised.
However the 24-year-old remains a highly rated player.
And, according to newspaper A Bola, Liverpool are speaking to Sporting director Bruno de Carvalho about the midfielder.
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Tue, January 24, 2017
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It is claimed a deal for Liverpool could cost them around £25million, with three years still left on his contract.
Liverpool have an abundance of options in midfield with Jordan Henderson, Emre Can, Georginio Wijnaldum and Lucas.
Following Saturday’s 3-2 defeat to Swansea, Jurgen Klopp expressed his frustrations over not being able to sign players in the window.
William Carvalho is one of Sporting's stars
“I understand it is absolutely normal, people ask whether we should have brought players in,” Klopp said.
“The situation is yes, on the one side pretty simple, but on the other hand it is pretty difficult.
“It is not that we don’t want to bring players in. We do. But the thing is, the players we want because we think they help us, the clubs don’t sell. It is not about money in this situation, it is the winter transfer market.
William Carvalho has been a target for Premier
The front page of Portuguese newspaper A Bola
“Clubs are saying ‘no we have half a year to go, we can not find another player like this, we prefer to take money in the summer, than a few pound more in the winter than whatever’. So it is pretty easy.
“You see the situation, it’s tight, it’s close, we know that, but if the right decision is not possible in signing the right player, then you cannot make the wrong transfer.
“It is not as if there are 20 players out there who could make this team stronger, who are running around and are available. That is the situation.”