Rudiger has one year remaining on his deal with the Blues and has flourished since his fellow German, Tuchel, was appoited in January.
In a glowing verdict of Rudiger, Tuchel said: "Nothing is better than what he is doing for a new contract. If he wants to stay at the club he has our full support. He is speaking with his performances and has been amazing.
"He is very brave and full of energy in his defending.
"He is leading by example and has a very positive aggressivity in him. This is what we like. When he can channel all this into top performances. We are all very happy to have him."