The young forward has been one of the key factors in the team's rapid rise in recent seasons, netting crucial goals last term as they finished in second place in the Bundesliga.
"We play in the Champions League," he said. "We offer Timo the chance to make the next step. We are totally relaxed."
Real's interest in Werner made the front page of AS on Tuesday:
AS English @English_AS
Real Madrid keeping an eye on Timo Werner and the return of the #ChampionsLeague dominate today's front cover of AS https://t.co/ZQ65PMhlTZ https://t.co/DT5yFHdVvk2017-9-12 07:35:09
In 2016-17, Werner, who joined from VfB Stuttgart in the summer of 2016, netted an impressive 21 times for Leipzig in the top flight, giving the team a clinical and dynamic dimension in the final third. The performances he has put in earned him a spot in the national-team setup for the first time earlier this year.
Senior international football has been easy for Werner to adapt to as well, grabbing six goals in eight appearances so far.
Football writer Alex Chaffer has been impressed by his development:
Alex Chaffer @AlexChaffer
Genuinely frightens me how good Timo Werner has become. What a finisher. So much speed, power and composure.2017-9-8 20:38:46
After the summer sale of Alvaro Morata, Madrid look a little short in terms of their options up top and a player such as Werner would give them a huge boost in this area of the pitch.
The challenge for any side trying to get the youngster would be convincing Leipzig to cash in on one of their prized assets.
Given how vital he is, how much more he can improve and the spiralling costs of players in modern football, getting Werner away from the Bundesliga side would be a costly exercise.
Real Madrid Eyeing Brahim Diaz
The article suggested links between Diaz and Los Blancos had previously emerged from television show El Chiringuito and have since been followed up.
"Diario Madridista says that if there's a club who could convince the player to leave, that's Real Madrid, and the good relationship between Florentino Perez and Sheikh Mansour could also help," Sposito wrote.
The 18-year-old is one of the brightest prospects in the City youth setup. As noted by Squawka Football, he was impressive when given a chance in the first team during pre-season:
Squawka Football @Squawka
17-year-old Brahim Díaz in pre-season for Manchester City: ⚽️ vs. Real Madrid ⚽️ vs. Spurs Bright future. 💫 https://t.co/RhaOFE5Enw2017-7-30 11:28:00
With so much attacking talent available to City manager Pep Guardiola, it will be interesting to see how Diaz is integrated into the senior squad at the Etihad Stadium. For a Spain youth international, though, interest from Real Madrid will always be tempting.
It would be no shock to see Los Blancos go after Diaz either. In recruiting the likes of Marco Asensio, Jesus Vallejo, Dani Ceballos, Lucas Vazquez and Theo Hernandez in recent years, they are evidently looking to assemble a crop of rising stars; the City youngster would fit right in.