In this paper we establish a likelihood-based inference procedure for estimation of cointegration rank of a generic fractionally cointegrated process. The procedure is based on a sequence of quasi-likelihood ratio tests, whose asymptotic distribution is derived and tabulated. The underlying quasi-likelihood ratio test statistic is constructed by approximating a short-run component in an underlying model with autoregressive term of order k letting k grow to infinity along with the sample size T at a suitable rate. As a by-product of our analysis, the asymptotic distribution of quasi-maximum likelihood estimator of order of fractional integration and degree of cointegration in the model is derived. The estimator is shown to be $sqrt{T/k}$ consistent and asymptotically normal.