Unspliced (pre-)mRNA is a small but non-zero fraction of the total. In principle, you could build gene models from your data, map the raw reads to the gene models, and identify those reads that contain insertions relative to the models. Note that this will also identify reads derived from low-abundance isoforms with alternative exon insertions, and those may swamp your pre-mRNA signal. You may be able to discriminate some of those by translating the encoded insertion - most (but not all) alternative exons will maintain the reading frame of the flanking exons.
You may also be able to discern the signature of conserved splice elements (donor and acceptor sites) in introns, but those require either a clean intronic data set to identify those elements or prior knowledge of those sequences. If you have any genomic sequence, you may be able to build a training data set from known intronic sequences (i.e., align your gene models to identify bona fide introns from gDNA sequence).