According to Official letter No. 5575/TCHQ-GSQL
dated August 21st, 2020, EU exporters are only required to have a REX number when they self-certify origin for shipments valued at over EUR 6,000. For a shipment valued at under EUR 6,000, any exporter may self-certify origin for this shipment without requiring a REX number.
Accordingly, in case a shipment has the proof of self-certification of origin certifying that the goods value declared on commercial invoice does not exceed EUR 6,000, the exporter is not required to have a REX number (except case where customs authority has grounds to determine that the actual transaction value exceeds EUR 6,000).