PCI-DSS rules generally require that any PAN stored be encrypted in such a way that it requires not one, but two authenticators to decrypt.
In practice, this would normally mean that even if you intend that the end-user is the only one with an encrypted copy, this would be insufficient from a regulatory standpoint. "Who" has a copy is irrelevant, in this respect. If decryption can be accomplished by a single key from the provider (i.e., you), and you cannot affirm that the device it's stored on is encrypted (that is, a client responding with a true/false about the filesystem encryption following a transaction request is not currently a capability of any mobile device I'm aware of), then you will have no way to declare the end-user devices out-of-scope during a PCI audit.
One scenario might work: if you have an application which generates and secures its own key for storing the card information, and which then can respond to your server-side payment application with a token for previously-used cards at that site, then you can (probably) satisfy the basic requirements. As long as the server-side application can satisfactorily store and retrieve the PAN upon presentment of a reference token during the transaction, you're fine. However, even in that case the CVC or CVV must be manually provided by the user— that is explicitly not allowed to be stored together with the PAN.
Having the end user store their own card may also possible, but no program or application can be allowed to request that data from the end-user and expect to receive the response automatically, unless you store a unique key for that user server-side for decryption of the PAN. This is why the current strategy is for Android and Apple to store "card details" and autofill fields when they recognize a request to fill out transaction data. That should be fine, but a pedantic auditor could easily demand that you have some way of confirming the end-user's device only works with an encrypted filesystem.
Long story short: you effectively just want a page whereby someone's mobile browser can work with "autofill" in a friendly way. You'll get the same results, without having to worry about additional PCI PAN storage limitations.