The Reds have been linked with a move for the 22-year-old this summer, with Jurgen Klopp reportedly a big fan of Werner.
The German coach also pinched Naby Keita from Leipzig last summer, and Rangnick has claimed following in his former team-mate's footsteps may not be the best choice for Werner.
“Keita was an outstanding player here, but he's still struggling in Liverpool,” the Leipzig boss Buli News.
“So far, he's not the player there that he was here. The surroundings must be right for Timo. That's the case here.”
Since moving to Anfield, Keita has struggled for form. The midfielder, who scored 17 goals in his last two seasons at Leipzig, is yet to net for Liverpool and has provided just one assist in 22 games.
Keita spent two years with Werner at Leipzig and could still prove decisive in luring the Germany international to Merseyside.
While Werner’s future remains uncertain, one thing that appears clear is that the forward will be leaving the Red Bull Arena soon.
With just 18 months remaining on his contract, and an extension looking increasingly unlikely, Werner could be available for a cut-price deal next summer, with Bayern Munich also reportedly interested in securing his services.
“We have gone to our financial limits with our [contract] offer,” said Rangnick.
“We know that he can earn more elsewhere, but he can also provide for himself for the rest of his life here. Financial aspects will not be the decisive factor, but rather the sporting perspective.
“We're trying to keep him. He knows he's very popular in the team, with the coach and the fans.
“He's a top player, and he has become one of the most exciting Bundesliga strikers in the country. He still has one-and-a-half years left of his contract, and I hope that he'll stay. But, in the end, it's up to him.”
Werner has netted 11 times for Leipzig in 19 league games this season and could suit Liverpool’s fluid system, should he join the club. Like Roberto Firmino, he operates as a central striker, but is known to drop into midfield and help with the defensive side of the game.