The aim of this note is to prove the existence of mild solutions for functional differential inclusion with infinite delay in a Banach space: $$\left\{\begin{array}{l}  x^\prime (t)\in Lx_t+F(t,x_t), & t\in [0,a]~(a > 0)\\ x(t)=\varphi(t), & t\in ]-\infty,0]. \end{array}\right.$$ The results are proved by using a variation of suitable constants formula with infinite delay and a direct application of topological transversality methods based on the degree theory for $\chi$- Lipschitz multimappings.