To tweak the Field of Dreams quote "Do it and the tools will come." Tools are not the solution, they are tools to aid the solution. You need the solution first.
Start running agile with a physical task board or if you absolutely need a tool, use something free like Trello.
The key is to show success using an agile framework (I'll assume Scrum) and show how using it gets better predictability, better quality, better visibility (nothing says visibility like a 3'x5' burn down chart on the wall to the bathrooms. While you're doing this, take a little hit to translate reporting to the legacy system.
Once you've got a track record of success, then you can point out how the successful development practices require translation to a legacy PLM software product and how it would save time and create more accurate reporting if you moved to a tool that supported the way you work.
Asking for Jire (or Rally or VersionOne) before starting agile is like asking for a Porsche before you learn to drive.
Edit: I realize I was pretty general. Start with one small team or project and do a simple agile conversion. Nothing fancy, nothing extreme, just a simple scrum implementation. Show it works small scale, but make sure the pilot isn't going to be unscalable. Doing a pilot with advanced TDD and Continuous Integration won't scale easily to the whole company. KISS Pilot will be your best approach.