yes, it depends on the context and where it is used in. 욕 from 욕심 means desire or eagerness to something. 욕망, 욕구, 탐욕, like these. and then 심 came from mind, think or heart, for example, 진심, 본심. so, if 욕심 is used in the context that describes selfish, self-centered, take too much from the limited resource, it can mean greedy. ex)쿠폰을 공평하게 1장씩 나눠 갖기로 했는데, 그 사람은 너무 욕심이 과한 나머지 혼자 2장을 챙겨갔다. but if it is used to show your goal, vision or hard-working attitude, it doesn't include negative meaning. ex)그 사람은 승진에 대한 욕심이 많다. thus, 저 욕심 많아요 - can be understood in both ways and we need more background or context to figure out what the exact meaning is. he/she is selfish and admit his/her characteristic or he/she is ambitious for business, career, or getting promotion. and if you want to say that person is ambitious, you can say 그 사람은 야망찬 사람이에요. but if you want to use 욕심 to express it, you might say, 그 사람은 일 욕심이 많은 사람이에요. so you add extra information that the person is ambitious about his/her own work or something like that, and not selfish. hope this could be helpful!

I'm not sure if they are similar to English words or not Anyway Greedy is literally 욕심있는, 욕심이 많은 Ambitious is 욕망 They are similar as the word 욕망 means you are not sitisfied with something so you want more But 욕심 is more often used :) I think this is just my opinion that 욕망 is often more negative than 욕심 like a big dream that you don't think to be able to make it even if 욕심 and 욕망 are similar haha. Or ... like things make you speechless haha

la palabra codicia y ambición siginifican lo mismo, son sinonimos, asi que yo diria que es negativo en ambas formas