The Daily Mirror believe that the Reds could be front-runners for Werner next summer.
The 21-year-old had been linked with a move to Bayern Munich, but RB Leipzig sporting director Oliver Mintzlaff appeared to rule them out.
“We had a pleasant lunch and dinner with FC Bayern, with Mr Rummenigge and Mr Hoeness. We talked about everything,” Mintzlaff told German broadcaster Sport 1.
“But we did not talk about Timo Werner. Therefore there is no enquiry or offer.”
Werner has started the season well, he has already scored six goals in nine games so far this season after notching 21 last term.