The 48-year-old actor and his Deadpool and Wolverine co-star guest presented Jimmy Kimmel Live in July and had a great time, and the Free Guy actor is keen to build on the fun they had and take their bond to an even bigger platform with the Academy Awards.
He told Deadline: "The Oscars, yes. This is something I really genuinely would love to do with Hugh.
"Yeah, we hosted Kimmel together, but we also had just kind of hit, 'F*** it' at that point, we were at the end of a long tour. We travelled in every country all over the world, and enjoyed every second of it.
"And we go to Kimmel, we didn't even remember the schedule, [as it was] so intense on the tour like that. And so we got to Kimmel, and we just got loose.
"And it was, I thought, kind of an interesting way to host it. It feels like those old AFI dinners where everybody would get up there — they go from decades and decades ago all the way up to present day.
"They look like what you sort of hope the Oscars could feel like, right? A bit of a roast, a bit of a loose kind of enjoyable experience. And, you know, it's getting harder and harder out there, I think, for telecasts like that to kind of exist, it's tricky."
However, Reynolds - who has daughters James, nine, Inez, eight, five-year-old Betty and 21-month-old son Olin with wife Blake Lively - admitted he and Jackman are unlikely to take the reins for next year's ceremony, which will take place on March 2.
He said: "So, one day I'd love to do that, I don't know about this year, but one day, yeah.
"A lot of things would have to happen that are kind of amazing. Part of it is that these movies like Deadpool and Wolverine, they consume my life, and I have four kids, and I want to be there.
"I want to see them, and they want to see me, and I want to walk into school with them, and I want to be able to be there present.
"And if I were to host something like (the Oscars) as someone who, you know, kind of feels a bit of intense sort of anxiety, I wouldn't be present mentally. I would be kind of constantly writing in my head, or projecting potentially tragic outcomes on the live stage."