"Send him a horse and he'll have the horse on the show and it will take a dump on the show and it will be hilarious," says Dave.
"For the purpose of this conversation, I have nothing but the highest regard for all of the talk show men and women - even Jimmy Fallon. I'll include him," Letterman said, setting up the story after O'Brien revealed he got a bizarre gift from Dave earlier this week.
When Letterman was "either fired or retired" from "The Late Show" on CBS in 2015, he sent Kimmel a box of his ties. But since Conan is "some sort of God on Mount Olympus who runs around telling people he went to Harvard," he decided to send the TBS late-night host something a little more grand.
"You know what I'll do? Send him a horse and he'll have the horse on the show and it will take a dump on the show and it will be hilarious," he said.
But in a weird twist of events, Letterman received a letter from Conan saying his wife actually loved the horse and wanted to keep it since she's an equestrian.
"Now I'm screwed because I was counting on him returning the horse and I get my money back," Letterman said.
The retired late-night host apparently forgot all about the horse until Conan appeared on the "Late Show" this week.
"I don't hear anything about it, until he shows up on 'Late Show' and now he's lost his mind," he said. "Conan will not shut up about the horse. And the horse had gone crazy. Something happened. Maybe it's from being around Conan all day. I don't know."
"So now he's complaining. There may be litigation and maybe I'll get a call from PETA," he concluded.
Conan previously told Colbert he heard Letterman was sending him a gift as a token of his appreciation. The late-night host assumed that probably meant a nice bottle of wine, but was surprised when he got a call from Warner Bros. security saying the gift arrived, but it was too wide to enter the gate.
"He's a car guy. I'm thinking he's giving me a vintage Porsche," Conan said.
The TBS late-night host then complained about the finances this "crazy" horse required, since he had to provide the animal with food and a place to live.
"By this point one of my children is no longer being schooled, this is costing so much. It's the boy - it wasn't going to work out anyway. He's good with his hands," Conan joked.