Rudiger is said to be holding out for closer to £10m net profit per year – a little under £200,000-a-week.
But it is reported that Real, along with Bayern Munich, will also struggle to meet those demands.
Paris Saint-Germain are named as potential suitors with Mauricio Pochettino keen to shore up his defence.
For Chelsea, losing Rudiger would come as a huge blow as the 28-year-old has started all but one league game this season.
A replacement would have to be signed, but Tuchel’s made it clear that he’s a big fan of working with Rudiger.