The dependence of the T-odd correlation on the effective Lagrangian parameters in the K^+ →π l νγ, l=e, μ decays is analyzed. It is shown that the introduced observable is perspective in a search for new physics in the vector and pseudovector sector of the Lagrangian. As for scalar and pseudoscalar sectors, the T-odd correlation studies will not allow one to improve current restrictions on parameters of models beyond SM.