I'm thinking specifically pre-modern, indigenous perceptions, not that of European explorers. In other words, what did the people who actually lived alongside them think of them. I am aware that similar questions have been asked but as far as I have seen most of them are from European sources or don't deal with folk understandings. Thanks!
Interesting question, I'm not an anthropologist but I have read one book in particular that covers your question (with a focus on Japanese folklore).
In Japan, there is an old idiom that says:
"A monkey is a man minus three pieces of hair"
The belief was that monkeys were trying to be human but didn't quite 'get it'; they were poor imitators.
There is also a 13th century Japanese folktale that goes like this:
The hard-working man worked in the field from early morning till evening to grow soybeans and red beans. One day he became tired and fell asleep, whereupon monkeys came and thought he was a Buddha. They gave him yams and other offerings and went back to the mountain. The man took the offerings home. Upon hearing this story, the wife of the lazy man urged her husband to do the same. The monkeys carried him across the river to ensconce him there. While they were carrying him on their arms, the monkeys said, "We should raise our hakama" and they stroked their fur to imitate the gesture of raising the hakama. Upon seeing this, the man laughed. The monkeys said that he was a man, instead of a Buddha, and threw him into the river. He was drenched, swallowed a great deal of water, and narrowly escaped his death. Upon hearing of the incident, his wife became enraged. "One should never engage in superficial imitation of others."
The story is meant to be somewhat ironic, because although the man was imitating a Buddha to get food - the monkeys were also imitating men. In this way there is a sort of relationship between men and monkeys, where the monkeys serve as mediators (teaching the man a lesson and teaching the reader a lesson).
I read these in 'The Monkey as a Mirror' (1987) by Emiko Ohnuki-Tierney, it's an interesting read about how the monkey has been viewed in Japanese culture across time.
"Orang" is Bahasa for "man" or "person"; "orang utan" is "wild man" or "man of the woods." If you've heard the idiom, "The Wild Man of Borneo," that's literally "orangutan" - an ape in Borneo that was named the "wild man."
Before the first specimens were identified, the story of the "orang utan" was put on a par with Pacific Northwest stories about Sasquatch or "Stick Indians", or Himalayan stories about the yeti (literally, "small, man-like animal").
Scientists are still undecided about another Indonesian cryptid, the "orang pendek" or "short man." Possibly a smaller great ape in the jungles of Borneo*, possibly an orangutan subspecies or just another description of orangutans.
^* Edit: Or, really, Sumatra.
I can remember reading a text about the Great Plains Indians which told a story about a Sioux raiding party that had traveled a long way to the south which found a forest in which there were very fierce little men who lived in the trees and who threw things at them. I can't remember the book, unfortunately, although it might have been Dee Brown's "Bury my Heart ....".
Try asking this in /r/AskAnthropology as well - perhaps it might be noted by anthropologists who know something about the topic but don't visit AskHistorians