Rudiger's current deal at Stamford Bridge expires at the end of the season, and it looks increasingly likely that he will leave on a free transfer next summer.
A who's who of Europe's top clubs are thought to be queueing up for the 28-year-old, and overseas clubs will be able to open talks with him from January 1.
Rudiger is reportedly asking for a £200,000-a-week offer from Chelsea - more than double his current £90,000-a-week wage - but could stand to earn almost £400,000 a week elsewhere, making him one of the world's best-paid defenders.
Chelsea are understood to have so far offered him £140,000 a week but have not returned to the table with a fresh offer since August and, while Tuchel stressed the Germany international's importance to the team, he also warned that the club must come first.
"It is super important and as I understood, like myself and everybody else, we absolutely accept the importance, we are fully aware of the importance of Toni and the role he is playing on and off the pitch. There is no doubt in that," Tuchel told reporters.
"And yes it is true nobody is bigger than a club, nobody is. This is a team effort, it is a team game, it is a strong club and it is also about the club.
"It is not about me, it is not only about Toni — and I mean that in the best way because we know what he is doing and we are fully aware of it. In the end, we need a bit of patience. I have no update right now."
Real Madrid are thought to be leading the race for Rudiger, but the likes of Manchester City, Liverpool, Bayern Munich, Paris Saint-Germain and Juventus have also been credited with an interest in his services. body check tags ::