Rudiger's Chelsea deal expires at the end of the season, and Blues boss Thomas Tuchel revealed at the weekend his fellow German had decided to reject a new deal at Stamford Bridge and join a new club fifa world cup 2022.
Rudiger is thought to be flattered and impressed by Real's pursuit. The Spanish giants were the first club world cup 2022 to formally express an interest in signing him this summer.
A number of clubs across Europe - including in the Premier League - remain interested in Rudiger but 2022 fifa world cup, while talks with Real are ongoing, he is set to move to the Bernabeu.
Rudiger's representatives held talks with Barcelona last month, while he has also been linked with Manchester United, Paris Saint-Germain and Juventus.
Remaining at Chelsea was a possibility for Rudiger, but the sanctions placed on the club's owner Roman Abramovich made talks over extending the 29-year-old's deal impossible.
"We gave everything - me and the club football world cup 2022 - but we could not fight anymore because of the actions. Without the sanctions we would at least be able to carry on fighting, but our hands are tied. We don't take it personally. It is his decision qatar world cup 2022.
"He is a key figure and will stay that way until the end of the season world cup football 2022. But it is disappointing. We will miss him a lot.
"He gives courage in the dressing room fifa 2022 world cup. The kind everyone is afraid of, but the kind to play 50-55 games at an outstanding level. He is a top defender in the last one-and-a-half years for me. We then need to find another solution."
Pressed on whether Chelsea will be able to replace Rudiger, Tuchel said: "In the moment not, because of the sanctions. Hopefully the sanctions will be the past 2022 football world cup.
"We had a connection from day one and he deserves my full support. I'm just happy to have had the chance to coach him in the team and the club did as well. We had offers, big offers and the club 2022 football cup tried everything but we cannot fight anymore. We have the sanctions, we can't continue. It is what it is.
"It would be ideal [for sanctions to be lifted before the transfer window] but even if we wish for it, you can't pull grass for it to grow faster. We have to deal with what the reality is. The sanctions are still in place and the situation is not cleared for next season. We try to focus on the last weeks."
Jorginho admits the centre-back will be a big loss for the team, saying: "He's been here a long time so if he leaves then we're going to miss him.
"He's a big personality and he's helped us a lot. We've had amazing times here; he's a good friend of mine and of course if he leaves everyone at the club world cup 2022 will miss him, not just me."
Asked what he will miss the most about Rudiger, the 30-year-old laughed: "His craziness. He makes me laugh a lot; all of his jokes and laughs we've had together - that's the nice part."
Jules Kounde has paved the way for a move to Chelsea this summer by telling Sevilla he remains determined to leave the Spanish club, the PA news agency understands.
Chelsea thought they had a deal wrapped up, only for Sevilla to dig in at the last with the switch falling through just before the summer's transfer window closed world cup.
Chelsea cannot make any new signings or complete fresh contract terms with existing players under the club's UK government sanctions.
Chelsea have lost clear ground in the transfer market due to the club's fifa world cup licensing constraints as a result of the sanctions on owner Roman Abramovich.
Since Rudiger came back into the fold, Chelsea have won the Champions League, UEFA Super Cup and Club World Cup, victories they owe in no small part to defensive solidity.
The security Rudiger provides is evidenced by the statistic that Chelsea have conceded twice as many goals (1.4) with him out of the team, compared to when he plays (0.7).
