Detect Magic would sense a Moderate or Strong Abjuration aura when looking at the Antimagic Field(AMF), but nothing within the field.
Despite being a sphere of antimagic, AMF is still a spell effect and produces an aura as anything would. Per Detect Magic, a 6th level spell would produce a Moderate aura, and its 8th level version produces a Strong aura.
Detect Magic's stated target is an area 60ft long, not a personal spell. Any range that extends within the AMF would be nullified. They would be unable to determine the source of the aura, unless they could see enough of the sphere to determine its center.
A further note, except in cases of GM Fiat, AMF will be centered on a creature. The spell states "An invisible barrier surrounds you and moves with you." Furthermore, there is no RAW item that has maintains an AMF, and the closest, the +1 Tower Shield Equalizer values the once per day use of AMF for 10 minutes at over 100,000g.
Rules as written, it is left to DM or the table for interpretation
Rules as written what you're supposed to do is look at Nondetection and Portent and decide for your table how it works. You're supposed to look at what the intent of Nondetection and the intent of Portent is supposed to be, which means you'll have to read and decide for yourself based on how you understand the rules and what works best for the fun and enjoyment of your table. That is 5e's rules philosophy.
I don't buy the "It doesn't say it is or it isn't, therefore it isn't." You can just as easily say, "It doesn't say it is or it isn't, therefore it is." Lack of evidence doesn't prove anything. The game rules do not claim to be comprehensive, and this is the natural consequence of that. This is the entire point the "rulings not rules" idiom is making. There is no burden of proof on Portent or Nondetection or the PHB as a whole to provide an answer. While that line of reasoning was implicit to 3e and 4e -- both editions that sought comprehensive and complete rules sets -- 5e actively does not do that. 5e D&D is often intentionally vague so as to leave rules open for interpretation and the system intentionally doesn't use keywords or raw mechanics. It does this so that players and DMs have the explicit freedom to interpret the rules for themselves and do what makes sense for that interaction. The designers know they can't possibly foresee every interaction in the rules, so they no longer try.
There is no clear answer by design. Yes, this means that asking, "What is RAW?" on RPG SE for 5e D&D is often a pointless exercise because the answer you should often get is, "RAW it depends on your table." This is why there are so many conflicting answers on RPG SE for 5e questions and why Sage Advice contradicts itself so often.
The rules are less important than the game. What Mearls and Crawford want is for players and DMs to stop asking WotC how to play and just make a decisions and play for themselves. If you make a mistake, admit it and make a correction. It's no less destructive than doing nothing until WotC makes a decision and then maybe changes their mind later.
You're expected to look at whole picture that the rules are giving you and to make a judgement call on what feels the most consistent and correct for your table. Is it reasonable for Nondetection to block Portent? Sure, it almost certainly is divination magic given that it's an ability of the Diviner subclass. How about a Ranger's Primeval Awareness? Well, that works like a spell, even consuming a spell slot, and it would have to be divination magic given the distance, so sure. How about a Paladin's Divine Sense? Hm... possibly, it's pretty close to Detect Good and Evil, but it's really described as the Paladin's senses. A Warlock's Devil's Sight? Hrm, hard to say. It's got elements that only True Seeing can accomplish, and Nondetection probably blocks True Seeing, but it's basically an improved Darkvision spell and that's not even Divination. So maybe partially? A Barbarian's Feral Instinct? Eh, that doesn't seem right, it's not magical. A Rogue's Blindsense? Yeah, probably not unless Blindsense is supposed to be magical, but I don't get that impression.
Best Answer
I present two different, independent arguments, hopefully at least one is helpful. (And a bonus tongue in cheek argument.)
Nondetection says it hides the target from divination magic.
Flavorful language in spell descriptions are rules too. Indeed, the entire spell description is the spell's effect. From the rules for reading spell entries:
The description of nondetection says:
Detect magic is a divination spell, and nondetection says it hides you from it. Case closed.
Victims of AoE spells are referred to as targets.
This isn't easy to find, but there is a rule in the PHB which specifically uses "target" to refer to someone affected by an AoE spell, in the section "Targeting Yourself" (emphasis mine):
Additionally, we see in the rules for Saving Throws (emphasis mine):
AoE spells are obviously in view here. Further, in the DMG's rules for Adjudicating Areas of Effect, we see (p. 249-250; emphasis mine):
In the rules for using miniatures on a combat grid, we see the following about areas of effect (p. 251; emphasis mine):
For a more specific example, the spell descirption of fireball even calls creatures it affects "targets":
Therefore, a creature under nondetection cannot be a target of detect magic, in the sense that the rules refer to victims of AoE spells as targets.
Mostly joke argument, but kinda for real.
Its called nondetection, obviously it defeats detect magic.