I wouldn't move a muscle. He does not apear to be alarmed enough to get up and move. Just looking as if he heard something. Perhaps there are other elk in the area?

I can't tell for sure but he appears to be bedded down.

I would sit still until he decided to get up and move. If he walked my way great I would wait until his head was concealed and draw and put one through his chest. If he decided to walk off and offer no shot I would probably give a hot cow mew or two when he wasn't looking my direction in hopes he would turn around and walk my way.