Can I pour a concrete footing on very wet base material?
I'd wait. You said a footer for a retaining wall. If the wall is 4' high or more and only holding back earth (no car or house surcharge,) then the footing should be about 3' wide. Also, the rebar should be on the side of the wall closest to the earth. 

The force from the earth will push on the wall and will make the wall and footer ROTATE about the footing. If this soil under the footing is soft, it will compact the soil and cause the wall to lean. 

By the way, don't forget to install a perf pipe at or near the bottom of the footing encased in drain rock.