From the perspective of someone with allergies: I'm usually acutely aware of my sniffling, so it can be mildly embarrassing and annoying when someone mentions it. So I'm glad you're being mindful of not putting them in an awkward position!
I do not recommend hinting around, like asking "do you need to blow your nose?" -- this comes across as very condescending, as if I'm a child who needs to be reminded how to take care of my own body.
Instead, if they're sniffling, let them know you have tissues if they'd like one: "do you need a tissue? I've got some in my bag". This is a polite offer (maybe I don't have any with me but didn't want to ask) and leaves the choice up to me (not pushy).
If they decline, you could hint a little: holding out a tissue, asking "you sure you don't want one?" when they start sniffling again. But, be aware that mentioning it repeatedly starts to feel like the first option (and honestly sometimes, like with a cold - I'd rather sniffle a bit than go through a million tissues and sandpaper the skin off my nose). So you'll need to weigh the irritation of listening to their sniffles (and/or if you think they're embarrassing themself in front of others) vs. how much you think they'd be irritated by your request.
However, if it's more of a visible problem, you can treat it in the same way you would tell them they had something in their teeth - a quick "hey, you might wanna blow your nose", with a discreet gesture to indicate usually gets the message across. This is pretty universally embarrassing, so regardless of feelings about sniffles I've always appreciated being made aware of this.