Eccentricity of a given ellipse is dependent on how stretched (flattened) it is. A circle is a special case of ellipse but with no eccentricity. If you stretch a circle into an ellipse of greater eccentricity, the foci will get separated along with it. This implies that as the ellipse gets stretched more and more, the foci gets further apart so is the eccentric.
From the above info we can deduce that as the distance between foci decreases, the eccentricity will also reduce.