We investigate theoretically the generation of the correlated squeezed state in the nonlinear coupler when the coherent optical fields propagate along the nonlinear coupler. We study the behaviours of the quantum fields generated from vacuum in the optical waveguides of the short-length nonlinear coupler by linearizing the quantum equations of motion around the corresponding classical solutions. The linearized treatment enables us to take into account the depletion of the classical fields and the influence of input conditions, which are imposed on the classical waves, on the generated fields. The degrees of squeezing in both optical waveguides in the nonlinear coupler are calculated numerically and their relations to the solutions of the classical equations of motion are discussed. The effect of the input relative phase between the classical optical fields on the output squeezing is also discussed.