Anthony split from Lopez in 2011 after seven years of marriage and their divorce is currently going through the courts.
The singer/actress has since been dating one of her former backing dancers, Smart, but Anthony insists there is no animosity between him and his ex-partner's new boyfriend.
He tells U.S. chat show host Wendy Williams, "It's great. As a matter of fact, we were texting back and forth two days ago. We're actually really, really good friends. From the very beginning.
"When you love someone and you care for someone... Jennifer and I, I don't say it lightly, we're great friends. You know, anybody that means anything to her means something to me.
"That's keeping it simple. Casper's a great guy. He's been great to my children. And I have nothing but respect for him, absolutely nothing but respect."
The former couple is parents to five-year-old twins, Max and Emme.