Caveat: IANAQSA, and this is more guesswork than usual.
Using the logic I used in this answer, the answer would seem to be no, as you're not "involved in payment card processing".
However, in your comment to @bobince's answer you state that your client "is saying we must be PCI-DSS compliant. Can they claim such?" Well, if they're subject to PCI DSS, then yes. It's in line with (v3) 12.8.2:
Maintain a written agreement that includes an acknowledgement that
the service providers are responsible for the security of cardholder
data the service providers possess or otherwise store, process or
transmit on behalf of the customer, or to the extent that they could
impact the security of the customer’s cardholder data environment.
Maintain a program to monitor service providers’ PCI DSS compliance
status at least annually
Now, it sounds like you're an application provider rather than a service provider. And even though you're not a "payment application" per se, this guidance probably applies:
PCI DSS may apply to payment application vendors if the vendor stores,
processes, or transmits cardholder data, or has access to their
customers’ cardholder data (for example, in the role of a service
There is some precedent saying, essentially: You don't have to maintain DSS compliance. But if you don't do so, then the burden of proving the compliance of the app falls upon your client. For that reason, clients often demand that application providers maintain DSS compliance, usually by choosing not to do business with providers that won't.