Werner has been in prolific form this season and is attracting interest from some of Europe's top clubs.
The German striker has scored 27 goals in all competitions so far this season and is tipped for a summer transfer away from RB Leipzig.
Barcelona are keen to sign a new, long-term striker to fill the boots of the now 33-year-old Luis Suarez.
They signed Leganes' Danish striker Martin Braithwaite this month in exceptional circumstances as they currently have a number of first-team players injured.
Manchester United, on the other hand, are looking to add firepower after it became clear that without Marcus Rashford, they are less threatening in the final third.
Ole Gunnar Solskjaer reportedly tried very hard to sign teenage striking sensation Erling Braut Haaland in January, but Borussia Dortmund won the race.
Werner, however, is thought to have reservations about both Barcelona and Man United - he would rather wait and see if Liverpool make a bid.
The 23-year-old has been heavily linked to the Premier League leaders of late and has commented on the interest himself.
"I know Liverpool is the best team in the moment in the world," Werner said to Viasport.
"When you’re linked with that team it makes me very proud."
Werner is believed to be very keen to play under his compatriot Jurgen Klopp, who he regards as the best coach in the world.
But Werner does worry that if he signs for the Reds, he could spend some of his peak years on the bench.
Liverpool's strong front three of Sadio Mane, Roberto Firminho and Mohamed Salah are almost untouchable.
Although, Firminho is 28 now and could be given a run for his money by the younger Werner.
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