The pair have agreed to get matching tattoos if Ricciardo finishes on the podium for Renault before he leaves the team at the end of this year.
With Ricciardo having delivered a strong fourth place finish in the Belgian Grand Prix, and believing his car can be even stronger in Italy this weekend, he is bullish about winning his bet.
Asked by Motorsport.com about how worried Abiteboul should be about getting his first tattoo, Ricciardo said “I think pretty nervous. I've just seen him now. I told him to stay alert over the next seven days.
“At least last year, Monza was an even stronger circuit for us: and if we are stronger there's only a podium in front of us.
“I'm not getting ahead of myself, or the team isn't, but I think we can go to Monza with confidence and aim high.”
Renault’s performance in Belgium came as the result of its car being much more competitive against its rivals in low-downforce configuration than it is when more wing is needed.
Ricciardo even reckons that had he not lost time behind Pierre Gasly and Sergio Perez after the early safety car in Belgium, that he could have challenged Max Verstappen for the podium already.
“I think if the strategy of Gasly and Perez didn't put a buffer between Max and myself, I really think I could have ran with Max for that last stint,” he said.
“He pulled away because obviously we lost time with the different strategy, and then we reeled a big gap in towards the end. So Monza, all going well, we should be pretty competitive.”
With Renault having had some mixed results so far this year, Ricciardo admitted he never expected to be threatening a Red Bull the way he did on Sunday.
“It was certainly surprising,” he said. “I knew we would have a decent car. But when I heard the lap times, and that the Mercedes was dropping off tails, I thought okay, maybe everyone's just saving their engines.
“But it sounded like they were genuinely struggling a bit and we were just getting faster and faster and faster. It was really encouraging that pace at the end.”
The details of the podium/tattoo bet are that Abiteboul can choose the location of the tattoo while Ricciardo can choose its design.
Speaking about what his plan was, Ricciardo joked that he had already seen some photoshopped images of Abiteboul with a face tattoo like Mike Tyson.
“I saw some mock ups of the Tyson face tat...on Cyril,” he said. “But I think he chooses the placement, so it's definitely not going to be on his face!
“I wouldn't be cruel and get him like a rubber duck or something. I'll get him, I think, something so it's a good memory, so I guess maybe the destination where the podium happens. So something to do with that, whether it's that circuit or that city in that country. We'll see.
“Or a shoe maybe, a Shoey. We will cross that bridge when we get there, but I am sure I will be flooded with ideas.”