Animals that use language are most likely those that have the greatest capacity for

insight learning

Explanation:

Insight learning was a theory that was formulated by German psychologist, Wolfgang Kohler  in 1920s, when he was studying the behavior of apes.

And, insight learning was described as a type of learning or problem solving that happens all-of-a-sudden without repeated trials or continuous practices.

Insight learning is very important because, it helps in solving problems through one's own efforts.

And ,language is known to be a means of communication. This could be verbally or through body gesture.

In this case, any animals that can either communicate verbally or through sign or action have greatest capacity for insight learning, that is solving problems on their own.