Jet and Mai have never interacted in the canon universe. It is impossible for this to happen in the future because Jet is dead.
Jai is a rather popular Avatar ship despite the fact that it is a crack pairing as the two have never met. Many fans feel that Jet and Mai would compliment each other well and pair them together as a "pair the spares" situation. Jai is commonly shipped along with Zutara as it solves the issue of Jet and Mai not having a significant other. Jai commonly rivals the Jetara and Maiko ships.