I agree that there isn't even a tiny hint in any of the books (LotR, Hobbit or Silmarillion) about Galadriel and Gandalf harboring any tender feelings towards each other.
Galadriel and Gandalf know each other, at least in passing, since the Years of the Trees in Valinor - since her birth. That's then thousand years plus some millennium or two. Gandalf knows all about her greatest shame, her deepest sorrow, and her curse. They are both Ringbearers, they are both members of the White Council. At this point he is one of the very few (in Middle Earth) who have seen Valinor (not her husband), the home she is banished from.
The bond may not be friendship, but even if it was camaraderie or familiarity, it has to be strong.