ion-icon is an Angular component. The popup expects strings (for title/subTitle) and that string won’t be interpreted by Angular so you can’t use a component in the popup.
But since the Ionic icons are rendered from the ionicons font file, you can create a css class to render the icon you want:
this.alertCtrl.create({
title: `Title with icon: <span class="icon-wifi"></span>`
}).present();
Then define the icon-wifi .css in app.scss (this has to be declared globally as the alert is not part of you component tag):
The important part here is the content. Since the icon comes from a fontfile, it means each icon has a character assigned to it. The content represents that character. You need to find out that character for the icon you want to use. One way is to open the Icons page and lookup the character in using developer tools: