Targeting the protein arginine methyltransferase 1 (PRMT1) has emerged as a promising therapeutic strategy in cancer treatment. The phase 1 clinical trial for GSK3368715, the first PRMT1 inhibitor to enter the clinic, was terminated early due to a lack of clinical efficacy, extensive treatment-emergent effects, and dose-limiting toxicities. The incidence of the latter two events may be associated with inhibition-driven pharmacology as a high and sustained concentration of inhibitor is required for therapeutic effect. The degradation of PRMT1 using a proteolysis targeting chimera (PROTAC) may be superior to inhibition as proceeds via event-driven pharmacology where a PROTAC acts catalytically at a low dose. PROTACs containing the same pharmacophore as GSK3368715, combined with a motif that recruits the VHL or CRBN E3-ligase, were synthesised. Suitable cell permeability and target engagement were shown for selected candidates by the detection of downstream effects of PRMT1 inhibition and by a NanoBRET assay for E3-ligase binding, however the candidates did not induce PRMT1 degradation. This paper is the first reported investigation of PRMT1 for targeted protein degradation and provides hypotheses and insights to assist the design of PROTACs for PRMT1 and other novel target proteins.