Bayern Munich are also admirers of the centre-back, who has been revitalised under Tuchel.
Talks have been ongoing throughout the summer and Chelsea had hoped to have Rudiger’s future secured by now. But it is believed he is holding out for closer to £200,000 a week, while Chelsea have indicated they will go as high as only £150,000.
Tuchel suggested the 28-year-old favoured remaining at Stamford Bridge, with the Chelsea manager also eager to keep hold of him, but the terms remain the sticking point.
“I hope that they find solutions, but it’s not only between coaches and players, and what we wish for,” he said. “And that’s why it’s between the club, the player’s agent at the moment.
“We hope that they find the solution. He plays excellent, and since a long time was very consistent, on a very high level.
“I think that Toni feels very, very good at Chelsea. He feels very respected by his team-mates and he feels the importance that he has in the team and in the squad.
“That’s well deserved because he delivers. He feels the love from the supporters when he plays.”
Rudiger was close to leaving Chelsea last year when deemed surplus to requirements by Frank Lampard, with PSG and Tottenham leading the chase for his signature.
But he became a vital part of Chelsea’s Champions League triumph in May after Tuchel made him a key component of his three-man defence.
The German manager insists the uncertainty over Rudiger’s future will have no impact on his performances.
“I feel him very calm and focused, and it’s not a distraction for him,” he added. “So everything is in place, and give things the time they need.
“Sometimes it needs a bit longer, sometimes things are very fast.
“He’s in the strongest league in Europe, in a big club, so not many reasons to change that. But in the end it’s between him and the club, and that’s in good hands.
“I am calm and relaxed, whatever has to happen will happen.”