I'm not sure I'm understanding this correctly.... is the squirrel standing on a wall, or a line of bricks on the ground....? I can see the bricks but is the area beneath it on a vertical or horizontal plane?I really don't think this one needs a background at all but, if you feel the need, the most I would suggest is a single lightly drawn twiggy weed. Sprouting somewhere behind its tail and mainly curving to the right to turn the eye back down to the squirrel. About as lightly drawn as your foliage on the extreme right - just enough to throw the squirrel forwards but not distinct enough (or detailed enough) to warrant any attention. Personally I'd leave the background bare. It won't be missed. If the focus is intended to be in the foreground then a background will only distract.
This Bearded Collie drawing of mine will, I hope, prove my point. It contains only foreground (and an arguable midground?) but no background at all.
I really like the your hair technique - it's got depth and true texture. Keep going!
MIKE
www.SibleyFineArt.com
www.Starving-Artists.net