Werner, who has scored 61 goals in 114 games for the Bundesliga outfit, has one year left on his current deal.
Liverpool have been linked with a move for another striker, with the 23-year-old’s name regularly cropping up in reports, while Bayern are no strangers to snapping up the best young talent in Germany.
“But so far, no club has reported their interest or said they would speak with Timo and want to sign him. It’s not a good idea for Timo to go into the final year of his contract, which could be difficult for his relationship with the fans depending on how his performance turns out.”
However, Rangnick is urging the 23-year-old to stay put at Leipzig next season – adding that when a “really big club” comes in for him, he can then leave.
“My opinion is that Timo fits best here, also in terms of style of play,” he added.
“If I were his advisor or father, I would clearly advise him to stay and extend his contract. When a really big club comes in for him and he wants to leave, he can still do that.”