No, the stars that make up a constellation are not near each other in space. They only appear close together from our perspective on Earth because they are in the same line of sight.

Imagine looking at a long road. You might see two cars that appear to be close together, but they are actually miles apart. It's the same with stars in a constellation. They can be vastly different distances from Earth and from each other, but because they appear close together in the sky, we connect them to form a pattern.