Speaking to Page Six, her representative simply said: "Absolutely not true!"
In his original comments, August claimed Will, 51, had allowed him to date Jada because their marriage - which began in 1997 - was no longer about "romanticism" and was instead a "life partnership".
August said: "People can have whatever ideas that they like, but what I'm not okay with is my character being in question … I'm not a troublemaker. I don't like drama. Drama actually makes me nauseous.
"I also don't think that it's ever-important for people to know what I do, who I sleep with, who I date, right? But, in this instance, it's very different, 'cause as I said there is so many people that are side-eyeing me, looking at me questionable about it.
"It's because people don't necessarily know the truth, but I never have done anything wrong.
"I actually sat down with Will and had a conversation. Due to the transformation from their marriage to [a] life partnership that they spoken on several times, and not involving romanticism, he gave me his blessing."
The 'No Love' singer also claimed his alleged romance with Jada - who has Jaden, 21, and Willow, 19, with the 'Independence Day' actor - "almost killed" him and made him into a different person after devoting his "full self" to her.
He added: "I totally gave myself to that relationship for years of my life. I truly and really, really deeply loved, and have a ton of love for her. I devoted myself to it, I gave my full self to it.
"So much so to the point that I can die right now and be OK with knowing that I truly gave myself to somebody … I really loved the person that I experienced that [with] and know what [that feels] like - if some people never get that in this lifetime.
"I'm shakin' right now because it almost killed me. Not almost. It did - it pushed me into being another person, my newer self. It. Broke. Me. Down."
