There is a strong need and demand from the United Nations, public institutions, and private sector for classifying government publications, policy briefs, academic literature, and corporate social responsibility reports according to their relevance to the Sustainable Development Goals (SDGs). It is well understood that the SDGs play a major role in the strategic objectives of various entities. However, linking projects and activities to the SDGs has not always been straightforward or possible with existing methodologies. Natural language processing (NLP) techniques offer a new avenue to identify linkages for SDGs from text data. This research examines various machine learning approaches optimized for NLP-based text classification tasks for their success in classifying reports according to their relevance to the SDGs. Extensive experiments have been performed with the recently released Open Source SDG (OSDG) Community Dataset, which contains texts with their related SDG label as validated by the community volunteers. Results demonstrate that especially RoBERTa achieves very high performance in the attempted task, which is promising for automated processing of large collections of sustainability reports for detection of relevance to SDGs.