The Delphi method has expanded steadily across scientific disciplines since its origins in the 1950s, yet consolidated indicators are still lacking for assessing the quality of its implementation and the reliability of its results. As a consequence, readers and users often struggle to evaluate the credibility of Delphi studies consistently and transparently. This paper seeks to address this challenge. It has a twofold aim: first, to determine whether leading Delphi scholars consider that Delphi reports should include a standardized set of quality indicators, and second, to identify what such indicators might be and order them by relevance and ease of application. To this end, we applied the Delphi method itself to a panel of 28 experts; these included many of the most prolific and highly regarded authors in the field worldwide. The results show a high level of consensus in favor of incorporating quality indicators more systematically into Delphi reporting. The study identifies the most critical indicators as being those that capture the quality of the expert panel, from different perspectives, reflecting the central role of panelists in determining the epistemic strength of Delphi outcomes. A second strongly-scoring group of indicators refers to the quality of the Delphi process itself, for which they evaluate the effectiveness of key processes for transforming individual judgements into a well-grounded collective opinion. This paper also provides an illustrative example of how such indicators can be operationalized and transparently reported in empirical Delphi studies.