I would say yes, just as long as you know who it was made by.

I got a bunch for my iPhone and nobody sued me for this reason.

because i learned that my phone can make transparencies of images just by holding down on the image and it pops out the subject. i did that, and put it as the background of my psvita, kind of cool that it can do that......wish the BIG N would allow us to put images on our backgrounds.

I even have Swordsoul background with "Mo Ye" on it on my computer as background screen, and Konami ain't sue me for doing that.

Is it for your own personal private enjoyment, something you like? Or are you planning on earning money from it? I don’t think for example Marvel lawyers are going to go after everyone who saves a deadpool pic to their image files or phones and such would not allow it to happen; Nor would anyone be able to create fan art. so long as it’s clearly indicated as such and the creator of the fan art did not try to sell the image.
So tldr, your phone’s wallpaper for your own private aesthetics falls under fair and acceptable use.
However if you intend to sell the image or put it on display for public viewing then I would seek permission.

Ah okay, was just making sure, thank you