Should I ask if he is forgetting things or having memory problems?

Who is this "he" carobles56? If he is your father or other elder relative that is different from if he is your peer. And a friend you see occasionally would be different from a Significant Other you are living with. So it would help to know more about the situation.

I'm answering as if this is a SO and you are living together.

If you have a good communication track record in your relationship, then I think this is an important topic worth communicating about. He is forgetting things. You think he might be aware of this. If he is, it is a serious worry, and something to share. When you are both calm and relaxed, bring it up casually. "I seem to notice that you are getting forgetful. Does it seem that way to you, too?" And then take your cue from his response. Certainly don't "accuse" him of losing his memory. Just bring it up in a way he can talk about it if he wants to.

If he knows he is having problems, encourage him to share his feelings. Assure him that you will stick by him and help him cope (if that is true). Discuss the possibility of consulting a doctor. Some causes can be corrected. If this isn't a correctable situation then the sooner it is addressed, the sooner the two of you can start coping, together.

Early diagnosis is an opportunity for a couple to grab the chance to do things they've wanted to before it is too late. I know of one couple who left the neurologist's office and went directly to a travel agent and booked a cruise they had been putting off.

If this is your parent or a more casual friend, my approach would be different. But giving someone the opportunity to talk about their worries and fears is a kindness, if they are open to discussion.

He knows he is forgetful. Do not point out his errors, it will only inflame his anger. Be prepared to offer hard proof of any items in contention, or just end the conversation. Debate does not work. Never say "I already told you that", just repeat the statement gently.

If a person is going through dementia or Alzheimer's, they might not realize they are forgetting thing.