The host hit the red carpet on Tuesday night, where he was asked by Access Hollywood about the beef between the two, after Burgess called Andy a "messy queen" for his line of questioning on the Bravo talk show.
"Are you guys feuding?" asked the reporter. "He might be, I'm not," replied Cohen, his first comments on the situation since Burgess put him on blast on both Instagram and Wendy Williams' show.
Then came the follow-up question: "Would he be welcome back on?"
"He's been on four times, sure," said Andy. "I don't think he would be ... he can do whatever he wants, I just don't want to offend him."
When Burgess appeared on "WWHL" Sunday night, Cohen said Tituss' costar Eddie Murphy "was very problematic for the gays" earlier in his career. Though Burgess had only praise for Murphy, he later called out Cohen for trying to pit them against each other in a lengthy Instagram post the following morning.
In his Instagram post, Burgess called Cohen "a messy queen" for his question. "Yes I said it! Don't care he knows either! He should remember his talk show isn't an episode of the 'Real Housewives of Atlanta.'"
"It's a place where artists come to talk about art and have a little fun. NOT a place to rehash old rumors or bring a star negative press," he continued. "Sunday was a display of ratchet behavior by a well connected man having a blatant disregard for one of his guests."
"If only time were taken to know who I am and not assuming that I am the character I play on tv, he would know how to conduct a proper interview with at all," the post went on. "I received 4 Emmy nominations for acting! NOT for being my self. He was lucky I had my wits and Christian values THAT day. Always keep it classy. Being friends with other talented celebrities doesn't make you talented it makes you friends with other famous celebrities! He should rip a page from Anderson Cooper and learn how to do his job."
Responding to a fan who said the show was "the most awkward #wwhl" they'd ever seen and thought the question was "relevant," Cohen responded saying, "I did too! Awkward is right."
Doubling down on his criticism on Williams' show, Burgess said his Instagram comments were not a "rant," but "just truth."
"I will not tolerate the dismantling of anyone's legacy, especially not my own," he continued. "Who we were speaking about has done a beautiful job being the comedic giant that he is. He has a wonderful movie coming out and I was not going to participate in talking about that."
"Tituss will not be trapped. We have way too much work to do, we have far more important things to talk about in this nation right now, especially what is going on politically," Burgess added. "I wasn't going to waste time digging up something that happened a while ago. We've all moved past from it and we've all learned from it."