The 18-year-old winger is a target for German champions Bayern Munich, who are on the lookout for replacements for Arjen Robben and Franck Ribery.
The Bavarians have tabled several bids for the teenager, the most recent of which is understood to be in the region of £35million.
Hudson-Odoi has remained tight-lipped on his future at Stamford Bridge, which appears to be bright after eight appearances for the first-team this campaign.
But according to Rudiger, the England Under-19 international is seemingly contemplating life in Germany.
“Of course, he asked me about Germany,” Rudiger told the media after Chelsea’s 1-0 loss to Tottenham on Tuesday night. “It was just a general question from him to know, because he is still young.
“I can advise him. But at the end of the day, he decides about his future.”
Hudson-Odoi was in Chelsea’s starting line-up against Tottenham on Tuesday night but has made the majority of his appearances for the club in the Europa League.
A move to Germany could do wonders for his development, just as it’s done for Arsenal’s Reiss Nelson – who is currently on loan at Hoffenheim – and former Manchester City youngster Jadon Sancho, who is flourishing at Borussia Dortmund.
Rudiger believes a move to Bayern would greatly benefit Hudson-Odoi but is adamant he can continue to grow in west London.
“He can develop as well here,” he continued. “You can see it from both sides.
“Of course, he can develop in Germany as well and don’t forget Bayern Munich is also a big club.
“It is something he needs to decide for his future. I wish him all the best, but for me I just wish he stays with us.
“We don’t need to speak about him too much. He is good, everyone knows that, everyone can see that.
“But he is still 18 and at that age you can’t look too far ahead. People have to give him time. For me he is an upcoming star, but he still needs to work hard.
“Of course, as a young player it’s very important to play. Where it is? I hope it will be here.”
Chelsea return to action on Saturday night, welcoming relegation-threatened Newcastle to Stamford Bridge.