There is no such list, but you could build one. You can find (multiple) frequency lists for many languages, and you could come up with a way to decide which frequency list to use (there are very many for English). I suppose you are thinking you might construct a list with entries like {day, Tag, jour, день, gün, siku, päivi, 日} where all of the words seem to mean the same thing and the words all end up on the top-1000 list in their respective languages (I don't know if they do, this is just a hypothetical example).

The problem is that the most frequent words in English (and many other languages) are things like "a, the, all, but, she", and these are not going to have correspondents in all languages. Plus, the various forms of the verb "be" or "do" and "don't" are each treated as separate words in some frequency lists. It would be more productive to define a subset of concrete nouns and "verbs" like "cat, dog, big, small, eat, walk" and get the N most frequent equivalents across languages. You must abandon the search for data in every language, but you could go for "as many as you can get". As a precursor to this exercise, you might try to come up with the N most frequent concrete nouns and verbs of English, filtering out proper names (unless you really want proper names to be included). Then do the same thing for Khmer. Then you have to decide whether "good" and ល្អ are "the same" in meaning (the Khmer word also translates "attractive").