could be roots that are under and through the base of the wall. Now it
looks like a pretty good sized tree, so if it went it could damage
your wall.

It depends on the quality of the wall.
Sincerely,
John A. Keslick, Jr.
Consulting Tree Biologist
www.treedictionary.com
and
http://home.ccil.org/~treeman


Those sort of trees have roots which are notoriously invasive and will
damage pipes and plumbing. Workmen that I meet usually have many stories of
too close eucaplytus trees causing cracks in house plumbings.

I'd also remove it.