This paper deals with a Hegeselmann-Krause opinion formation model with time-dependent time delay. Under a smallness condition on the time delay size, we prove exponential convergence to consensus for general interaction coefficients without assuming any restrictions on the derivative of the time delay functions. The related continuity-type partial differential equation, obtained as mean-field limit of the particle model when the number of individuals tends to infinity, is also analyzed. These results extend and improve previous analysis in [12].