@Petalomine I don’t think you can do it with alerts. The alert's functionalities are very limited. You can try it with a modal, passing a custom component (that can have ngModel in it) to the modal.
The modal docs: https://ionicframework.com/docs/api/components/modal/ModalController/
Although it seems that for now the modal occupy the entire screen and is a bit difficulty to style it to occupy just a part of the screen.
There’s a discussion about it here: