As soon as Michael Strahan announced in April that he was stepping down from Disney-ABC’s “Live! With Kelly and Michael” to move to “Good Morning America,” many viewers had one thought: Anderson Cooper!

Then that was pushed aside, as the fallout over Mr. Strahan’s departure briefly took over the Internet when it turned out that co-host Kelly Ripa was not given any notice, and she refused to show up for work. It was all (pretty much) resolved, but Mr. Strahan hightailed it out of there in mid-May — about four months earlier than planned.

Naturally, the rumor mill has since been buzzing about a possible replacement, with the CNN anchor’s name at the top of the list. On Wednesday and Thursday, Mr. Cooper (or “Coops,” as Ms. Ripa likes to call him) returned to guest-host the show and made a great case for why he’s the front-runner.

The main reason: He and Ms. Ripa are great friends in real life and their easy banter is clear proof. On Wednesday’s episode, the two devoted much of the desk segment to a recap of their Memorial Day weekend, as Ms. Ripa took her family to spend time at Mr. Cooper’s Connecticut home. Apparently there was an incident with an inflatable golden swan, which proved quite challenging for Mr. Cooper when he tried to climb on top of it in the pool. Maybe you had to be there.

Clearly, the two go way back, and Mr. Cooper has guest-hosted with Ms. Ripa many times before. Mr. Cooper — who turns 49 this week — even has a birthday close to Ms. Ripa’s son Joaquin, and they talked about how Mr. Cooper attended Joaquin’s laser-tag birthday party and had more fun than all of the kids.

On Thursday’s episode, they continued in the same vein when Ms. Ripa made fun of Mr. Cooper for his terrible performance during an aerial hoop workout on the show Wednesday. (His CNN newsroom colleagues found it hilarious as well.) The audience loved it.

So why can’t Mr. Cooper sign a contract ASAP? First, there’s the whole “he hosts a show every night on CNN” issue. “Entertainment Tonight” reported this week that Mr. Cooper would love to co-host “Live!,” but unnamed sources say both Disney-ABC and CNN are “hesitant” to let that happen, especially given how involved Mr. Cooper will be with the presidential election.

Over at People magazine, a Ripa source says that “When Regis (Philbin) left, the person Kelly wanted more than anyone else was Anderson Cooper, but he was busy launching his own talk show.” Of course, that show quickly flopped — so while Mr. Cooper has a packed schedule, he still has some free time now.

Still, the People source cautions, the fact that Ms. Ripa and Mr. Cooper are such close pals could hurt the show. What if they talk so much off-camera that they waste all their best anecdotes before they’re in front of the audience?

Make no mistake: This speculation will continue until there’s an official announcement. Other hosting rumors include everyone from Alec Baldwin to Mario Lopez to Us Weekly’s new report that the next co-host could be a woman. Although if you want to bet on it, Mr. Cooper might not be the worst choice.

First Published: June 3, 2016, 4:00 a.m.