The 48-year-old CNN correspondent and 42-year-old Extra host expressed interest in replacing Michael Strahan on Live! with Kelly and Michael following word Strahan will leave the talk show in May.
"I love Kelly," Cooper said Thursday on Watch What Happens Live. "Kelly is the heart and soul of that show and it's going to go on and continue to be great. I wish Michael the best in his new endeavor."
"I'm very happy at CNN. It would be a dream to work with Kelly, but nobody's offering anything," he said when asked if he'd take the position.
Lopez, meanwhile, called the rumors "flattering" on Friday's episode of The Ellen DeGeneres Show. The television personality said he's heard his name tossed around and seemed to confirm he's in talks for the job.
"I love Kelly. I've guest hosted with her a few times. She's awesome," Lopez said. "I actually did a movie with her husband, Mark [Consuelos], who's a really good guy. I'm looking forward to going back and [guest hosting again]."
"I've got to go over everything with Mrs. Lopez. She's the real boss of the house, so we'll see what she has to say," he added of his wife, Courtney Laine Mazza.
Cooper hosts the CNN news show Anderson Cooper 360. He and Ripa are longtime friends who first met when he filled in for Regis Philbin on Live! with Regis and Kelly. Ripa called herself "lucky" to have Cooper as a friend on WWHL in 2014.
Lopez is known for hosting Extra, America's Best Dance Crew and The X Factor and has guest hosted Live! with Ripa several times. Strahan joined the talk show in 2012 and will make his final appearance May 13.