Neres is one of the biggest talents in Dutch football with the Brazilian ripping up the Eredivisie with Ajax.
But the Merseyside clubs are not alone in the race to sign the 22-year-old.
Borussia Dortmund will try and take him to Germany if they lose Jadon Sancho at the end of the season, according to reports.
Paris Saint-Germain are said to be making the most noise about a player rated at around £40million.
Mercato claim the winger, who has eight goals and 11 assists to his name this season, is being very closely watched.
But they suggest Liverpool have not put forward an official offer - yet.