Doctors saw a slight glimmer of hope for Bobbi Kristina Monday morning — but they remain clear she’s not out of the woods.

Sources connected to the Houston family tell TMZ … doctors were testing BK’s brain reaction to different stimuli, and saw “minimal response” during one of the tests. We’re told doctors view this as a very slight improvement — but it’s enough to delay any immediate discussion of turning off life support.

As we’ve reported … the situation has been bleak, and we’re told just last night the family started discussing funeral arrangements.

Bobbi Kristina’s been in a medically induced coma since Saturday … when she was found unconscious in her bathtub.