The reference to ‘third-country national’ entails that nationals of EU Member States would not fall under the personal scope of the QD.
It should be clear that everyone has the right to apply for international protection. However, in accordance with Protocol (No 24) on asylum for nationals of Member States of the European Union, part of the consolidated version of the Treaty on the Functioning of the European Union, ‘Given the level of protection of fundamental rights and freedoms by the Member States of the European Union, Member States shall be regarded as constituting safe countries of origin in respect of each other for all legal and practical purposes in relation to asylum matters.’
Examining applications by nationals of EU Member States. Although this would rarely arise in practice, the protocol provides that applications by nationals of EU Member States may be ‘taken into consideration or declared admissible for processing by another Member State’ in some specific circumstances. See full text here.
Stateless persons with former habitual residence in another EU Member State. It should be noted that stateless persons with (former) habitual residence in an EU Member State are not specifically included within the scope of Protocol No 24.