Not really, no. There are certain types of pokemon that can communicate with people, generally psychic pokemon or ones with very strong latent psychic abilities.

[Armin can talk with his Lapras, but that took a long time to establish.]

But other than that, people can't really talk to pokemon. You learn to understand them, of course, when you have worked with them for a long time, but it's never as clear as direct speech. It's more of a body language thing.