He does.

When Izuku met up with Momo and Ochaco again, he took them aside and said, "Hey... Can we talk about something?"

"Sure, what's up?" Ochaco replied.

Izuku quickly explained to Ochaco that All Might had mentored him personally after taking an interest in him before the entrance exams, and after she asked why he was telling her about it, Izuku replied, "I kind of want someone outside of the harem to confide in about our secret... All Might and I are also keeping a secret of sorts that I want to ask him permission to confide in with both of you."

"What, you his secret love child or something?" Momo asked, making Izuku sputter.

"N-no, nothing like that!" he protested, making Momo giggle.

"I had to ask," she replied. "But are you sure it's okay? Can we actually trust him with something like this?"

"Momo, it's All Might of all people. Do you really think he'd try to take your powers for himself or something like that?" Izuku questioned.

"No, I'm more worried he'd decide to try and confiscate the lamp, or otherwise try to consider our actions wrong," Momo wrang her hands a bit.

That... Was an actual possibility, Izuku had to admit. Still... He highly doubted All Might would be the type to judge their relationship... At least, once he got over the skepticism about the magic thing, and it all being consensual. And he just couldn't stand the thought of continuing to keep something like this from someone who had given his all to help him, mentor him, even give his Quirk away to him. Nor the thought of keeping Ochaco and Momo in the dark about One For All.

"...I'm prepared to take that risk," he said finally.

"...we'll follow your lead, Izuku," Ochaco nodded firmly.

"Alright... If you trust him that much, this might be for the best," Momo sighed, but obviously still worried about this blowing up in their faces.

...

All Might was in his office, going over the paperwork to grade the battle trials, currently in his skinny form. He was currently uncertain about what grade to give Young Bakugo. On one hand, he had acted brashly and recklessly, but on the other hand, he had also shown impressive talent in combat. That maneuver he did to go up and over Young Midoriya and catch him off guard was executed perfectly. He didn't want to be too hard on him either. He seemed to have something of a large, but potentially fragile sense of self worth. Someone with potential, but in **** need of a careful, but firm hand to guide him. He ultimately settled on a C, possibly too generous, but also making sure to try to put some constructive criticism on the paper.

He heard a knock on his door. "All Might? It's me," Izuku's voice came in. "Ochaco, Momo and I would like a word with you."

All Might stiffened and sighed. If it was just Izuku, this would be easier. With the other two though, he'd need his muscle form. He considered for a second, and decided he could manage about fifteen more minutes today. Twenty if he pushed it. And he trusted Izuku to see the warning signs if he was in danger of losing it, and find an excuse to end things early if needed. Bulking up, he put on his grin. "Come in!" he called.

As they entered, he couldn't resist a bit of playful teasing. "So, to what do I owe this pleasure? This wouldn't happen to be about relationship advice, would it? I'm afraid I wouldn't be much help with that, despite my popularity, I've never really been on a serious date!" he laughed.

Izuku and Ochaco blushed heavily at the insinuation. "No, nothing like that... Actually, kind of," Izuku said, taking the lamp out of his bag. "We need to talk..."

With that, he began explaining everything. About how Momo had become and embraced being a genie, became his, and eventually brought Ochaco into the fold.