Unless you're asking something truly outrageous, it's almost always fine to ask for something, provided that you do so respectfully and that you're prepared to take no for an answer.
The fact that it's a single Monday works in your favour. The fact that you didn't ask about this when you handed in your notice works against you, as does asking about this so late into your notice period as I'm assuming you've already started it. But it's perfectly possible for your manager to decline your request and you need to be prepared to accept that. You can phrase it like this:
Since I have a vacation day left and my final day would fall on a Monday I was wondering if it would be possible to use that vacation day then, so my last day in the office would be the Xth while the Yth would be a paid vacation day.
Whether they allow it or not is a different matter and down to company policy, your workload and the relationship with your management. It's very common for US companies to not respect accrued PTO when someone resigns, though some states have laws requiring them to pay those out. Notice periods are much longer in Europe (months, not weeks) and it's very common to use remaining vacation days for the final X days of your notice period. So you run the risk of them actually putting your final day on that Friday and not paying out your vacation day.