The dictionary definitions to which you refer actually differ slightly.
Have an eye/a good eye for something means that someone is good at noticing something. The dictionary definition gives the following example sentences:
Ernest has an eye for detail. (Ernest is good at noticing detail.)
...
But @Kman3 I've heard the sentence "he has got an eye for ladies" about a lustful man who was attracted to all gorgeous women. How would you define it here?
@A-friend Since, in some male social circles, it is seen as a "talent" to form relationships with beautiful women, he's got "an eye for ladies" because he has this "talent" -- he's good at noticing gorgeous women.
Well @Kman3 I see. Well, let me clarify my intention bringing up another scenario. Two close friends are talking to each other. One of them says: "my husband doesn't seem to be interest to me anymore. He often gets home late and often texts on his phone." Her friend says: "Maybe, he has got an eye for someone else (another woman)." Or "Maybe, he is eyeing someone else (another woman)." Which one seems to be correct here?
@A-friend Out of your two sentences, the second one seems to be correct. You could say "has got his eye on someone else" instead to show that the husband has interest in another woman.
Aha Kman3. The just let me know how these two sentences differ in meaning? "He has got an eye for someone else" VS "He has got his eye for someone else"
I see @Kman3. Just can we omit "his" in "He has got his eye on someone else" and say "He has got an eye on someone else" or it is a fixed term and I cannot use "an" instead of "his"?
@A-friend From what I can find, both seem to work. I think using a possessive pronoun works best (your, his, their...), but I guess that's personal preference. See this source and this source.
Aha, then in my original question I could definitely say: "He has got an / his eye on you". So the correct answer would be "A" with changing the preposition from "for" to "on". Do you confirm @Kman3?
@Kman3 as you know I have brought up 4 scenarios. Let us check them again.
Scenario 1)
1) Lucas is totally into you. Whenever a guy buys something so expensive it means .......... 2) We are just friends Nancy. Why are you looking at me that way?! 1) Me and you both know the truth. Just be careful. You don't know him yet.
a. he has got an / his eye on you. b. he's eyeing you.
In scenario 1) as you mentioned, I can use both.
Just @Kman3 let me know if they are interchangeably in this sense.
Scenario 2) Regarding a lustful man who is attracted to all women we can say:
a. He has got an / his eye on ladies. b. He eyes ladies.
Regarding the second scenario, still I have not quite sure which one is the correct option.
Scenario 3) Two close friends are talking to each other. One of them says: - My husband doesn't seem to be interest to me anymore. He often gets home late and often texts on his phone. Her friend says: - Maybe,...............
a. He has got an / his eye on someone else (meaning: he has an affair with another woman)
b. He is eyeing someone else (meaning: he has an affair with another woman)
1) Look at that guy opposite you Susana. I'm sure he is checking you out. 2) Really? 1) Yea, I noticed that he had stared at you many times! But he doesn't look a gentleman. It seems that he's just looking for a lady for fun. 2) How do you know that? 1) Just look at his loud pants. 2) Huuum! 1) Anyway, I am sure................
a. he's got an / his eye on you. (meaning: "he is looking at you in a lustful way "OR "he is sexually attracted to you".)
b. he's eyeing you.
This is my last scenario which I am not quite sure which one is correct.
@A-friend Scenario 1, I think (a) and (b) both work; Scenario 2, these both seem unnatural but I would choose (a); Scenario 3, I personally would prefer (a), but I think (b) also gets the point across; Scenario 4, I think (a) and (b) both work.
Discussion between Kman3 and A-friend
Discussion between Kman3 and A-friend