I use Hybridization Probes with FAM and LightCycler Red 640, the setup of the qPCR is 2 min at 95º and then 40 cycles with 15 s at 95º, 30s at 58º and 30 s at 72º then there is the dissociation stage. So the problem has to be in the initial cycles.
But I don't know how to avoid this basal fluorescence.