Former UFC light heavyweight champion Jones is expected to make his return to the octagon later this year.
Jones had been hoping to make his heavyweight debut against Ngannou, who holds the UFC title, with the fight rumoured to take place in late June or July.
UFC heavyweight champion Ngannou kept hold of his belt after beating Ciryl Gane at the Honda Center in January.
Ngannou won the UFC belt from Miocic after knocking the American out in their rematch in March last year.
However, Ngannou has undergone surgery on his right knee that will keep him out of action for the rest of the year, forcing Jones to look elsewhere instead.
UFC chief White has confirmed that Jones is one step closer to returning to active competition and has identified Miocic as his ideal opponent for that bout.
White told TMZ: “Listen, people have been talking about how awesome this card is, and I was just telling somebody the other day our lineup for this summer is incredible.
“So I’m hoping that Jon Jones is going to be a part of that lineup this summer.
“Stipe makes sense.”
White said in an interview last month that Jones ‘could come right in and fight for a title’.
Speaking to ESPN, he said: “I haven’t thought about it at all, but yeah, it sounds like something we would do,”
“Not until we know what Francis is going to do or what’s going to happen.
“But if that’s the case, if he ends up sitting out for a year, Jon could come right in and fight for a title.”
White has admitted that Jones hasn’t always been the easiest to deal with amidst ongoing contract negotiations after several high-profile run-ins with the law.
He previously said: “It’s like it’s not even shocking anymore.
“When we bring him here it’s almost expected.
“You can’t even get him in Las Vegas for less than 12 hours to induct him into the Hall of Fame. It’s a problem. This guy’s got a lot of demons, man. A lot of demons.
“Is it really shocking anymore? It’s really not. It’s become not shocking.
“It’s almost like, ‘Uh oh, this guy is in Vegas, what’s gonna happen today?’
“You want to hope that the guy is better and that won’t be the case, but he proves that every time he comes to this town that he can’t handle this place.”