For a class of asymmetric multivariate exponential volatility models we establish the strong consistency and the asymptotic normality of the Whittle estimator of the parameters under a variety of parameterisations allowing for long-range dependence in the volatility dynamics. We present results for both the continuous and discrete Whittle estimator. We contribute to the long-memory statistical literature by establishing the convergence of quadratic forms of vector linear processes whose innovations need not be identically distributed and whose spectral density function might not be factorable.We assess its finite sample properties with a Monte Carlo simulation and compare them with those of the the maximum likelihood estimator of the parameters, showing that in some cases they perform comparably. An empirical application, using three market indexes (FTSE100, S&P 500 and Nikkei 225) suggests the potential of the model to capture the joint dynamics of asset returns volatilities.