And Cooper is definitely interested, another source tells ET, but may need CNN's permission to do the show.
Actor Neil Patrick Harris, who's already proven his hosting skills, is reportedly another strong candidate.
"Producers loved Neil Patrick Harris when they were looking before," the production source tells ET. "He was a frontrunner, and he has less going on now than he did three years ago during the search that ended with Michael getting the gig."
As for why Strahan left the show, sources tell ET that the decision was not exactly surprising, though it happened a lot sooner than expected. "He just has so much other stuff going on ... he was losing interest," one source says, citing his multiple gigs at Good Morning America and Fox Sports.
"Live! was never going to be a forever job for him," another source adds.
Good Morning America also apparently offered Strahan more opportunities. The 44-year-old former NFL pro will start working full-time for GMA in September and will become a co-anchor, but is not replacing anyone, a source tells ET -- rather, he'll continue handling more of the types of stories he was already doing in his former correspondent role.
"They provide something different for him and they give Michael a platform that he couldn't do at Live! -- tell stories, connect with people," one source says. "GMA saw an opening and they took it. He appeals to everyone."
Sources tell ET that there was also tension between Strahan and 45-year-old Ripa, as well as between Strahan and long-time Live! executive producer Michael Gelman.
"Michael and Kelly have not been getting along recently," one source tells ET. "They got along great in the beginning -- but not so much lately."
However, Strahan had nothing but positive things to say about his time at Live! in his statement on Tuesday, and thanked Ripa personally.
"My time with Live! With Kelly and Michael has been transformative, and my departure will be bittersweet," he said. "Kelly has been an unbelievable partner, and I am so thankful to her and the entire team. I am extremely grateful for the amazing support I've received from all of the fans."
"I look forward to continuing to work with the incredible team at GMA," he added. "It is an exciting opportunity to be able to bring unique stories and voices to the audience."