In the present study, machine learning algorithms are applied for modeling transport coefficients in strongly nonequilibrium reacting gas flows. As a model case, the problem of a hypersonic flow of a five-component air mixture around a sphere is considered. Various approaches for an application of machine learning methods, such as linear regression, k-nearest neighbors, support vector machine, regression tree, random forest, gradient boosting, and neural network (multilayer perceptron) are investigated. For the transport coefficients regression modeling the combination of machine learning methods with the finite volume method is constructed. The machine learning regressors are trained on the accurate numerical data given by one-temperature approach of the kinetic theory. The results of trained models are compared with approximate formulae of Blottner-Eucken-Wilke model. The results of different machine learning methods are analyzed in terms of the relationship between the obtained accuracy of calculations and the overall speed of calculations. The overall time of dataset formation and model training is estimated. The design of the constructed multilayer perceptron is discussed. The machine learning methods considered in the article can be used for the engineering problem such as design of high-speed aircraft, as well as for modeling of flows around complex shape bodies.