The most natural way is, in my opinion, to intervene into the process of instantiating of EntityListener.
This way significantly differs in Hibernate pre-5.3 versions and post-5.3 ones.
1) In Hibernate versions earlier than 5.3 org.hibernate.jpa.event.spi.jpa.ListenerFactory is responsible for EntityListener instantiation. The instantiation of this factory can be intercepted if you provide your own CDI-based javax.enterprise.inject.spi.BeanManager. The CDI interfaces are (unnecessary for Spring DI world) verbose, but it's not difficult to implement Spring BeanFactory-backed CDI Bean manager.
@Component
public class SpringCdiBeanManager implements BeanManager {
    @Autowired
    private BeanFactory beanFactory;
    @Override
    public <T> AnnotatedType<T> createAnnotatedType(Class<T> type) {
        return new SpringBeanType<T>(beanFactory, type);
    }
    @Override
    public <T> InjectionTarget<T> createInjectionTarget(AnnotatedType<T> type) {
       return (InjectionTarget<T>) type;
    }
    ...
    // have empty implementation for other methods 
}
and the implementation of type-dependent SpringBeanType<T> will look like this:
public class  SpringBeanType <T> implements AnnotatedType<T>, InjectionTarget<T>{
    private BeanFactory beanFactory;
    private Class<T> clazz;
    public SpringBeanType(BeanFactory beanFactory, Class<T> clazz) {
        this.beanFactory = beanFactory;
        this.clazz = clazz;
    }
    @Override
    public T produce(CreationalContext<T> ctx) {
        return beanFactory.getBean(clazz);
    }
    ...
    // have empty implementation for other methods 
}
Now, the only thing left is to inject into Hibernate Configuration Settings our implementation of BeanManager under a property name javax.persistence.bean.manager. There are, probably, many ways to do so, let me bring just one of them:
@Configuration
public class HibernateConfig {
    @Autowired
    private SpringCdiBeanManager beanManager;
    @Bean
    public JpaVendorAdapter jpaVendorAdapter() {
        HibernateJpaVendorAdapter jpaVendorAdapter = new HibernateJpaVendorAdapter(){
            @Override
            public Map<String, Object> getJpaPropertyMap(){
                Map<String, Object> jpaPropertyMap = super.getJpaPropertyMap();
                jpaPropertyMap.put("javax.persistence.bean.manager", beanManager);
                return jpaPropertyMap;
            }
        };
        // ...
        return jpaVendorAdapter;
    }
}
Just remember that two things have to be Spring beans:
a) SpringCdiBeanManager, so that BeanFactory could be injected/autowired to it;
b) your EntityListener class, so that line return beanFactory.getBean(clazz); will be successful. 
2) In Hibernate versions 5.3 and later things are much easier for Spring beans, as @AdrianShum very correctly pointed out. Since 5.3 Hibernate uses org.hibernate.resource.beans.container.spi.BeanContainer concept and there is its ready-to-use implementation for Spring Beans, org.springframework.orm.hibernate5.SpringBeanContainer. In this case, just follow its javadoc.