There are some clever tests described in The Language Puzzle on primates that (paraphrasing 14 hour long audiobook so forgive any mistakes.) indicate no primate

There are some clever tests described in The Language Puzzle on primates that (paraphrasing 14 hour long audiobook so forgive any mistakes.) indicate no primate other than humans and a couple of immediate predecessors (based on archaeological evidence) have much in the realm of abstract thinking abilities using their own communications, a few primates raised and taught forms of human language cannot progress very far without any of the facilities of language present in normal two-three year old development. The book is focused on how humans evolved language so other species are not covered, there is obvious verbal and gesture based communication in primates but it concludes not enough of the components of physiology that enable human language are present(both brain and vocal anatomy).