The design of turbulence optimized stellarators has so far relied on three-dimensional equilibrium codes such as VMEC in order to find the minimum of a given objective function. In this work, we propose a complimentary approach based on the near-axis expansion to compute the geometry parameters of neoclassicaly optimized stellarators used in turbulence studies. As shown here, the near-axis expansion can be a reasonable approximation of the geometric parameters relevant for turbulence and stability simulations of the core of existing optimized stellarator designs. In particular, we examine the geometry coefficients that appear in the gyrokinetic equation, the drift-reduced fluid equations and the ideal ballooning equation. This approach may allow for the development of new stellarator optimization techniques significantly faster than conventional methods.