So I'm not sure if I am fully answering your question because of the way it is being asked. If someone is moving towards another individual, of course there will be less time between when the sender speaks and the receiver receives. So yes, I guess you will hear the message faster if you are approaching each other than if you were both stationary. But this is only due to the fact that the other person is now closer.
But maybe what you really mean to ask is what would the differences in sound be. The Doppler Effect will come in to play, and if the relative speed is fast enough, you will hear a difference in pitch of the other person speaking. This is a purposeful design in things like sirens because as the ambulance is approaching you, the whine gets higher, which attracts your attention more. Frequencies and modulations are picked to make this effect even more noticeable to the human ear.