My impression is that the observed Higgs potential is not in fact compatible with asymptotic safety.

See the discussion at ncatlab.org/nlab/show/Higgs+field#AsymtoticSafetyOrNot summarizing p. 17-18 of

- Dario Buttazzo, Giuseppe Degrassi, Pier Paolo Giardino, Gian Giudice, Filippo Sala, Alberto Salvio, Alessandro Strumia, "Investigating the near-criticality of the Higgs boson", JHEP12(2013)089 (arXiv:1307.3536)

What is the case is that the observed Higgs potential stands out as being right on the line of meta-stability ncatlab.org/nlab/show/Higgs+field#MassAndVacuumInstability

This is compatible with asymptotic safety to first order. But it does not seem to be compatible to higher orders.