The Absolutely Fabulous legend plays "immoral" and "psychotic" prison governor Margaret in the forthcoming programme, which focuses on Horgan's character being wrongly jailed for the murder of her employer.
Speaking to reporters including Digital Spy, the comediennes agreed that Saunders had been part of their "dream cast" and admitted that they ended up pleading for her to take the role.
"We were begging her to do it," Pulling creator Horgan said. "After we did our pilot, we kind of honed in on Margaret as a character and thought that Jennifer would just be perfect.
"We're obsessed with her really a little bit and we are going to be her friends one day."
Walsh added: "She was sort of, like, our dream cast. When you write stuff, sometimes you [think], 'Well, that would be Philip Seymour Hoffman', and you know you're never going to get him. With Jennifer, when we were writing, we were writing in her voice."
The duo also praised Call The Midwife actress Bryony Hannah, who stars as Horgan's dopey, arsonist cellmate.
"We must have seen about 500 [actresses for the role]," Horgan recalled. "It took someone really, really charming and really funny to get it right."
"As soon as we saw her, we were all sort of in love with her," Walsh said. "She was so delightful to work with."
Although a second series of Dead Boss has yet to be commissioned by the BBC, Horgan confessed that she couldn't help thinking about future storylines.
"It's hard to switch your brain off," she said. "You just go, 'Oh, that could be series two' about everything."
Walsh continued: "You're left on a huge cliff-hanger. There's in no way a conclusion in episode six."
Dead Boss airs tonight (Thursday, June 14) at 10.30pm on BBC Three.