Why not handle your requirements in Jira? It is easily possible if you keep in mind the following things:
- have different card types (i.e. Jira issue types) like portfolio requirement, requirement, user story, story task, defect
- clearly define what card type to use on which level
- establish a governance model around, e.g. who is allowed to create a new card type
- maybe collect all incoming requirements in a distinct project
- link all issues so that you have tracebility
- use versions for release planning
To give an example, imagine you want to implement a text editor. You would probably define portfolio requirements like printing support, copy & paste, desktop integration, etc. Afterwards, you could refine each of those portfolio requirements further.
Together with product management, you will decide what portfolio requirements to tackle in the next major release. So you can create versions and assign your requirements to them. Also, for requirements to be implemented next, you probably want to refine them, e.g. create user stories and link them to the parent requirement.
You can establish a governance model around your requirements, e.g. that product management must sign-off a requirement before R&D is allowed to implement them. So you can define the required states for each card type.
The big benefit of having everything in Jira is that you can do nice reporting on all aspects. Everything is linked and you got full tracebility.
(I'm currently working in a large software company, where one of our development branches is doing their complete requirements management just with Jira. Of course, they use Confluence for software specifications by linking those documents from the respective Jira cards).