New Blues owner Todd Boehly has been filling up the role himself ever since Marina Granovskaia left this summer.
Freund came up as the ideal candidate for the position and held talks with Boely earlier this month but he has decided to remain with the Austrian outfit.
Freund has been instrumental in Salzburg's recruitment drive since his appointment in the 2015/2016 season, overseeing the signings and development of players like Erling Haaland, Takumi Minamino and Karim Adeyemi.
But Chelsea will have to turn their attention elsewhere, with Salzburg confirming Freund is going nowhere after extensive talks.
In a statement on the official club website, general manager Stephan Reiter said: "Christoph Freund has been performing wonderful work for us for many years, and only recently extended his contract to 2026.
"I can hereby confirm that he will remain FC Red Bull Salzburg sporting director. He informed me about the interest of Chelsea, of course, and we have spoken about it on a personal level with some good discussions.
"The fact is that he will remain our sporting director! He has not made a request with us to leave."
Freund himself added: "As I have already confirmed in interviews, Chelsea have been interested in hiring me.
"When a big club like that shows interest, it is an honour not only for me and the work of FC Red Bull Salzburg, it is also a situation that requires a number of personal considerations.
"I came to the conclusion that I am in the best place at FC Red Bull Salzburg, and a move was out of the question for me.
"We are in the middle of a really intensive phase, and we have big challenges ahead in the Austrian Bundesliga, Cup and Champions League – my full focus and concentration are directed on those now."
