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The new contract would have made the German the highest paid defender in the club’s history.
But they have admitted defeat in their attempts to keep him - opening the door to a move to Real Madrid as a free agent in the summer.
Chelsea were desperate to keep hold of Rudiger, who has established himself as one of the best in his position in Europe over the past season and a half.
But with a host of contracts up for renewal, the decision was made to set a limit in the case of the Germany international, at the risk of setting a dangerous precedent.
N’Golo Kante, Jorginho and Mason Mount are all due for talks over new deals, with Rudiger’s set to be used as a benchmark for future negotiations.
There have also been concerns within the club that more players will seek to run their deals down in a bid to earn even more lucrative contracts.
Rudiger will join out of contract Andreas Christensen in leaving Stamford Bridge - which will mean the club having to pay in the region of £100million to replace two pivotal members of last season’s Champions League-winning team.
While the current takeover and Chelsea’s inability to offer new contracts due to sanctions placed on Roman Abramovich have been cited as a reason for Rudiger’s decision to go - the feeling within the club is that he had plenty of time to agree to the deal on the table before now.