The Germany international has a contract with BVB until June 2017, but has a limited fee release clause that allows him to leave for €25 million in the summer of 2015 and Bayern are closely monitoring the 25-year-old's situation.
The reigning Bundesliga champions previously already signed Mario Gotze and Robert Lewandowski from Dortmund and Kahn feels it would be the knockout blow if they signed Reus, too.
"It would probably be the knockout blow if Reus would now leave Dortmund for Bayern as well," Kahn told reporters.
"It would not just hurt Dortmund on the pitch. You should not underestimate things like this. It would be a huge blow for a club like Dortmund.
"It would also affect them psychologically and leaves them wondering why they cannot hold on to their best players."
Reus picked up a serious ankle injury in his side's 2-2 draw with Paderborn at the weekend and will be out of action for the remainder of 2014.
The attacker has netted six goals in 11 appearances in all competitions so far this term.