Last month, Leakes blasted the former View co-host by claiming that she "wouldn't spit on Star if she was on fire".
In an interview with Parade, Jones insisted that publicly sparring with the Real Housewives of Atlanta star is beneath her dignity.
"Honestly, I refuse to be a part of it," she said. "I had no choice but to be connected to NeNe throughout the competition."
The TV personality added: "Since we are not friends, we weren't before and we're very different personalities, so we won't be after - I don't feel the need to engage in a public way."
Jones, who has worked as a legal analyst for NBC and Inside Edition, further explained that her trouble with Leakes derived from their opposing strategies on how to win The Celebrity Apprentice.
"I'm a strategic thinker, which I do think is probably what frustrated NeNe the most in the competition. I approached this like it was a job," she said. "This was my obligation to work hard and to achieve certain goals."
Jones continued: "I used intelligence, strategy, my legal background, and my vast resources in terms of who I know and how we do things in New York City. I used it to my advantage and to the advantage of my team. That's something that I brought to the table and I think that's probably what was frustrating."
Yesterday, Donald Trump insisted that the cast of the reality competition's upcoming season are "crazy".
The Celebrity Apprentice premieres on March 6 on NBC.