A photograph of the two, now deleted by the designer, took social media in a tizzy on Sunday.
Gurung has now released a statement on Twitter clarifying that Karan is just his "dearest friend".
He wrote: "Can we have some humour and levity please. I feel very saddened and disappointed to need to say this, but to officially set the record straight: I am not in a romantic relationship with Karan Johar," he wrote in the post.
The designer said his Instgram post of Karan and him was done with "humour and my absolute love of Bollywood, it's melodramatic flair and the one and only Madhubala".
"It has subsequently been misconstrued as Karan an me being in a relationship. Karan is one of my dearest friends."
He added that he turns to Karan, whom he described as his mentor, guru, confidante and a big brother, at the time of need.
"We've seen each other through our respective highs and lows. Karan is someone I deeply admire and respect . Not only has he been there for me, he's been there for my family as well. I admire his wit, compassion, and his empathy for this world," he added.
Gurung wrote that he loves Karan but only as a friend.