If the old system works reliably and is valuable to its users, if maintenance costs will not be reduced by introducing a new system, if the new functionality will not have any financial impact, if there are no savings for moving the software from an old platform to a new platform, if there are no regulatory or non-compliance risk with the old system, why do you want to replace it in the first place?
Why do you say the system is out of date? Just because it is written in an old language? If there is no maintenance risk, then why replace it?
Will the system run faster or will be able to run on less expensive hardware if you rewrite it? If yes, maybe you have a case.
Remember that rewriting the system will bring you back to square one on the learning curve, you will replace a reliable and debugged system with one that may have many bugs and may not implement correctly the current functionality.