In this seminar, I will explore possible connections between the causal sets and asymptotic safety approaches to quantum gravity. In the first part of the seminar, I will discuss how to construct geometrical objects in causal sets. Motived by functional renormalization results on asymptotically safe quantum gravity, I will discuss the construction of a causal sets action, including curvature square terms. This action paves the way for future searches of asymptotic safety from causal sets. In the second part of my seminar, I will discuss recent functional renormalization group results for scalar fields with dynamics inspired by causal sets. In particular, I will show that the renormalization group flow leads to a connection between the Higgs mass and the non-locality scale introduced in the definition of a d’Alembertian operator in causal sets.