Jurgen Klopp's side have been the team most strongly linked with a summer deal for Werner, although there is also thought to be interest from the likes of Barcelona, Chelsea, Manchester United, Real Madrid, Juventus, Inter Milan and Bayern Munich.
Bild reports that the latter of those teams have seen their hopes dashed, though, with the 24-year-old unwilling to join another German club.
Werner has a £52m release clause in his current contract at Leipzig and is understood to favour a move to Liverpool in order to work with Klopp.
The Germany international has scored 27 goals and created a further 12 in 36 appearances across all competitions this season. body check tags ::