No. The EU Guidelines to Good Manufacturing Practice for Medicinal Products for Human and Veterinary Use; Part II Basic Requirements for Active Substances used as Starting Materials does not contain a reference to a Qualified Person. It is the Quality Unit that has this responsibility.
But the QP is required to in an EU marketing application that the API has been manufactured in accordance with Part 2 of EU GMP. It is important to emphasise that it is the QP who is certifying the final drug product and who has to give the assurance that the API has been made in accordance with the relevant GMPs. Hence the QP must have access to appropriate documentation including supplier audits (not necessarily by the QP themselves) together with a Quality Contract (Agreement) signed by both parties, to assure her-/himself that the API does comply with the valid standards.
However, some Member States may have differing national regulations that might require QPs for certain APIs, e.g. in Germany those APIs derived a human, animal, microbiological source, and manufactured by biotech methods.