  In this paper, we analyze the Schwarzschild-like wormhole in the
Asymptotically Safe Gravity(ASG) scenario. The ASG corrections are implemented
via renormalization group methods, which, as consequence, provides a new tensor
$X_{\mu\nu}$ as a source to improved field equations, and promotes the Newton's
constant into a running coupling constant. In particular, we check whether the
radial energy conditions are satisfied and compare with the results obtained
from the usual theory. We show that only in the particular case of the wormhole
being asymptotically flat(Schwarzschild Wormholes) that the radial energy
conditions are satisfied at the throat, depending on the chosen values for its
radius $r_0$. In contrast, in the general Schwarzschild-like case, there is no
possibility of the energy conditions being satisfied nearby the throat, as in
the usual case. After that, we calculate the radial state parameter,
$\omega(r)$, in $r_0$, in order to verify what type of cosmologic matter is
allowed at the wormhole throat, and we show that in both cases there is the
possibility of the presence of exotic matter, phantom or quintessence-like
matter. Finally, we give the $\omega(r)$ solutions for all regions of space.
Interestingly, we find that Schwarzschild-like Wormholes with excess of solid
angle of the sphere in the asymptotic limit have the possibility of having
non-exotic matter as source for certain values of the radial coordinate $r$.
Furthermore, it was observed that quantum gravity corrections due the ASG
necessarily imply regions with phantom-like matter, both for Schwarzschild and
for Schwarzschild-like wormholes. This reinforces the supposition that a
phantom fluid is always present for wormholes in this context.
