In this work we consider a general function for the c2 term that appears in the conventional expression for the holographic dark energy in a FLRW curved spacetime. The cut-off prospective is inspired in the apparent horizon length. By exploring the slowly varying condition for the c2 term, we obtain a range of validity for this holographic proposal. Under these considerations can be found that this holographic cut-off is adequate to describe the late cosmic evolution. Additionally, by considering some values constrained with the use of observational data for some cosmological parameters in the context of dark energy models, such as the deceleration parameter or the parameter state, can be shown that this holographic model remains close to the Λ CDM model.