The 20-year-old rising star defeated former world title challenger Dillian Whyte, 37, in the first round of their bout last month, and Davison has now said he would accept a fight with Itauma and the undisputed heavyweight world champion, 38.
Speaking about a possible match-up for Itauma with The Cat, Davison said: “I would take it. I would. I think it's a win-win.
“As much as Moses hasn't boxed anybody like Usyk, I don't think Usyk's boxed anybody like Moses. I think he would openly say that himself.
“It's something he [Itauma] would be up for. I think he's got the mindset: if you're taking a dive [into the deep end] you might as well take the dive. Hopefully we may end up in a world title fight.”
Itauma is looking for one more fight before the end of the year, and Davison thinks Jermaine Franklin, 31, or Filip Hrgovic, 33, would be a good fit.
The trainer said: “Those are the two on everybody's lips. They're not interested and it's the same for pretty much all of them, so it's difficult.
“It's difficult to get these opponents at this moment in time. They're not interested, they don't want to play ball.
“They just want so much money to box him it's hard to get the opponents. The next fight, if we can pull something off and get somebody like that we're all for that. That's what we're after, the same as everybody else.
“But if not I suppose we'll have to drop down a level and try again in the new year maybe.”
Usyk is to defend his championship against the winner of Joseph Parker, 33, vs Fabio Wardley, 30, though the four belts could become fragmented if the title becomes vacant.
Davison said: “It's a real possibility. [It depends on] Usyk, if he decides to keep hold of one, if any, [of the belts]. Definitely interesting times.
“The heavyweight division's on fire.”
Davison also trains Anthony Joshua, 35, though he doesn’t think a fight between AJ and Itauma will happen.
He said: “That won't happen. There’s a lot of respect there. I don't think it's necessary.”