Imagining unreal stuff This is probably the most adequate stackexchange for this question.

Is it possible to imagine something that does not exist, explicitly or implicitly, in our universe?

Exclude things such as a Unicorn for example, that's just a horse and the corn is from other animals who have such an "organ". Other stuff might be just an application of the laws of nature. Our images of extraterrestrials usually involve hands, eyes, holes as nose etc.. which we do know of.
The best known examples of impossible objects are one of the following (but there are a multitude of others around). 

Of course they exist as you see right in front of you on your screen. Yet, that is in 2D space. If you imagine these objects to be 'real' matter, so imaginary physical objects, and imagine tracing the cube's ribs (Fig. 1) with your finger, or the ribs of the triangle (Fig. 2), or the tripod (Fig. 3) you are imagining the impossible. Such an object cannot exist in 3D space. Likewise, if you imagine tracing the water in the waterfall (fig. 4) falling and flowing back up, against the laws of gravity, you definitely imagine an impossible thing, as such a scenario can only exist in 2D space - our mind tricks us into assembling an impossible 3D perception out of a 2D image.   

Escher has made many of these impossible objects that exist only in 2D space.

Reference
Escher op reis. Frederico Giudiceandrea 


Fig. 1. Impossible cube. source: SLU Math


Fig. 2. Impossible triangle. source: Brain Teaser


Fig. 3. Impossible tripod. source: Piscesdna 


Fig. 4. Escher's Waterfall ('Waterval'). source: Hanover College