Despite helping his side win the Ligue 1 title last season, there remains the possibility of a summer exit due to the French club's financial problems.
Barcelona have been linked with an approach for the Portugal international, who has two years remaining on his current contract.
However, according to reports in Spain, Liverpool are the favourites to wrap up a deal for the 23-year-old before the end of the current transfer window.
The report suggests that Barcelona are unable to meet Lille's asking price, said to be in the region of €40m (£33.92m).
Liverpool are allegedly hopeful of reducing that valuation if they remain patient in the hunt for Sanches's signature.