Under the assumption of pathwise uniqueness, we prove Strassen type functional local law of the iterated logarithm for solutions of stochastic differential equations in modulus spaces defined in term of the Young function $M_2(x) = \mathrm{exp}(x^2) − 1$ and the modulus of continuity $\varphi_0(t) = (t \log(1/t))^{1/2}$.