National trademarks cannot be converted into an EU trademark, as the mark in question has to be evaluated again before being granted protection on the grander level. Hence a new application has to be submitted with the EUIPO.
On the other hand, EU trademark registrations can be converted into national-level applications if the EUTM has been rejected, withdrawn, or has ceased to have an effect.
Suppose a EUTM application is successfully opposed in one or more member countries, and the applicant is prevented from obtaining the EU trademark. In that case, the EU application can be broken down into national applications, and the applicant can apply for (selected) individual national trademarks in countries where a successful opposition hasn't blocked the trademark application.