Ex-goalkeeper Kahn is hopeful the Austria international Alaba will sign new Bayern deal.
Manchester United and Chelsea are now being linked with a move for Alaba.
Former Germany international Oliver Kahn insists Bayern Munich are "optimistic" of keeping versatile David Alaba despite reports linking the defender with a move to the Premier League.
Various tabloids have linked the Austrian with a move to Manchester United, Chelsea, and Manchester City, but Pep Guardiola's Cityzens have already spent a reported £41million on Nathan Ake.
However, Bayern legend Kahn is convinced the 28-year-old will agree to extend his contract, which is set to expire in 2021.
"We are currently in frequent talks with David Alaba and his advisors," Kahn, who is to become Bayern's CEO at the end of next year, told reporters.
"Of course, I can't talk about the content, but I think we're getting closer [to an agreement]. The atmosphere during the last conversation was very pleasant. We're doing everything we can to keep David.
"At the moment, I'm optimistic that we can keep David."
Serge Gnabry scored twice to help Bayern beat Lyon 3-0 on Wednesday as the Bundesliga giants secured a Champions League final showdown with Ligue 1 heroes Paris Saint-Germain.
And, Khan said of the inform Gnabry: "He is a player who has developed in the last few months," said Kahn. "His performance curve goes up from year to year. He is far from reaching the top but is really good, he produces top performances.
"It also has to do with the coach. That is one of Hansi's strengths. He can deal with different types of players, always finds the right words.
"As a coach, you always have to deal intensively with characters, with people and players."
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