Possible with DM blessing

Part of the wording is, "you or a creature you choose can ride the steed". While you might be able to envision a "horselike" creature that could carry the mule, the mule itself is incapable of the verb definition of "riding".

"sit on and control the movement of..."

The mule would just be cargo which means it is likely just draped over the back. Which brings up the other definition.

"a journey made on horseback, on a bicycle or motorcycle, or in a vehicle."

Which would aptly describe what you're wanting; the mule is "along for the ride".

It just depends on if you and your DM see ride as a noun or a verb.It just depends on if you and your DM see ride as a noun or a verb.

But beyond verbal gymnastics, there is the question of how to get the mule on the steed and keep it there. My experience with mules would suggest they would not like to be in the saddle and carried and would keep kicking and flailing to get off.

The Phantom Steed does come with a saddle, but it may not prove to be enough when the creature doesn't want to be there in the first place.

So it's really a "Talk to your DM" case, and if you can make a good story, you might have a chance.