Nucleic acid probes are valuable tools in biology and chemistry and are indispensable for PCR amplification of DNA, RNA quantification and visualization, and downregulation of gene expression. Recently, triplex-forming oligonucleotides (TFO) have received increased attention due to their improved selectivity and sensitivity in recognizing purine-rich double-stranded RNA regions at physiological pH by incorporating backbone and base modifications. For example, triplex-forming peptide nucleic acid (PNA) oligomers have been used for imaging a structured RNA in cells and inhibiting influenza A replication. Although a handful of programs are available to identify triplex target sites (TTS) in DNA, none are available that find such regions in structured RNAs. Here, we describe TFOFinder, a Python program that facilitates the identification of intramolecular purine-only RNA duplexes that are amenable to forming parallel triple helices (pyrimidine/purine/pyrimidine) and the design of the corresponding TFO(s). We performed genome- and transcriptome-wide analyses of TTS in Drosophila melanogaster and found that only 0.3% (123) of total unique transcripts (35,642) show the potential of forming 12-purine long triplex forming sites that contain at least one guanine. Using minimization algorithms, we predicted the secondary structure(s) of these transcripts, and using TFOFinder, we found that 97 (79%) of the identified 123 transcripts are predicted to fold to form at least one TTS for parallel triple helix formation. The number of transcripts with potential purine TTS increases when the strict search conditions are relaxed by decreasing the length of the probe or by allowing up to two pyrimidine inversions or 1-nucleotide bulge in the target site. These results are encouraging for the use of modified triplex forming probes for live imaging of endogenous structured RNA targets, such as pre-miRNAs, and inhibition of target-specific translation and viral replication.