Portugese newspaper A Bola claimed earlier this week that Liverpool are in talks with Sporting director Bruno de Carvalho about the Euro 2016 winner.
And bookmakers BetStars have responded by pricing Liverpool as 15/8 favourites to sign the 24-year-old midfielder before the January window shuts.
Liverpool favourites to sign Sporting Lisbon ace William Carvalho
Jurgen Klopp to beat Pep Guardiola to William Carvalho signing
Premier League rivals Manchester City were frontrunners for the Portugal international's signature last week but their odds have since fallen.
Jurgen Klopp's side will reportedly have to fork out at least £26million to land Carvalho, who has three years remaining on his Sporting contract.
“Liverpool have emerged as the new favourites to sign Sporting Lisbon midfielder William Carvalho," a BetStars spokesman said.
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"Last week Man City were 6/4 favourites to sign the Portuguese star but talks have slowed between City and Sporting leaving the door open for the Reds to jump in.
“Jurgen Klopp is reportedly lining up a £26million bid to get Carvalho in to anchor the Liverpool midfield.
"Carvalho to make the switch to Anfield is currently at 15/8 at BetStars.”