At Sunday night's BET Awards pre-show, Kim told DJ Envy the news.
"Not going to say who against, but would you do a Verzuz?" DJ Envy asked Kim on the red carpet.
"Yes," she replied.
"Is there anybody that you'd do it against? Or are you just ready for anybody?," he continued.
"Nicki," Kim said.
The two rappers have gone at each other before, with Kim calling Minaj a "wannabe" and "Lil' Kim clone."
It's speculated Minaj has referenced Kim in some of her songs, including "Tragedy."