We define a notion of tracial $\mathcal{Z}$-absorption for simple not necessarily unital C*-algebras.
This extends the notion defined by Hirshberg and Orovitz for unital (simple) C*-algebras.
We provide examples which show that tracially $\mathcal{Z}$-absorbing C*-algebras need not be $\mathcal{Z}$-absorbing.
We show that tracial $\mathcal{Z}$-absorption passes to hereditary C*-subalgebras, direct limits, matrix algebras,
minimal tensor products with arbitrary simple C*-algebras.
We find sufficient conditions for a simple, separable,
tracially $\mathcal{Z}$-absorbing C*-algebra to be $\mathcal{Z}$-absorbing.
We also study the Cuntz semigroup of a simple tracially $\mathcal{Z}$-absorbing C*-algebra and prove that it
is almost unperforated and weakly almost divisible.