Rudiger is most likely to join Real Madrid this summer as a free agent after failing to agree fresh terms on his expiring contract at Stamford Bridge.
Sanctions placed on Chelsea following outgoing owner Roman Abramovich's links to Russia president Vladimir Putin meant the club were unable to offer new contracts to their players.
Chelsea are set to come under new ownership after American billionaire Todd Boehly agreed a deal to buy the club.
It has been suggested that Rudiger's situation could have been influenced by sanctions on Chelsea but the Germany international insists that is not the case.
"I don’t want to go too deep into things," he told reporters at Wembley on Saturday, after Chelsea lost 6-5 on penalties to Liverpool in the FA Cup final, their third consecutive defeat in the competition's showpiece.
"There was a chance but sanctions were not the problem.
"It’s been five years with ups and downs as normal. There were a lot of positive things, but that's why I'm even more frustrated because I wanted to have a different ending.
"It's about both sides. Chelsea have been great to me and I have been great for Chelsea. I am very, very thankful, both me and my family.
"I became a man here. My kids were born here and everything. London, and especially Chelsea, will always be special to me."
Rudiger joined Chelsea from AS Roma in the summer of 2017 and has won one FA Cup, the UEFA Champions League, UEFA Super Cup, FIFA Club World Cup and Europa League in his time at the club.
