We're not discussing a systematized Magic. So nothing can specifically be
ruled in or out of it as an absolute. Endless associations are present and
nothing at all in LotR is specifically not associated with 'magic'.
Certainly knowledge, wisdom and power are deeply and widely associated with
'magic' (i.e. the ability to effect the world through creative power (or some
definition like that)).
Gandalf's library reasearch is an integral element in the Council of Elrond.
And to me the Council was very 'magical' indeed because it turned on magical
knowledge of the nature of the universe far beyond what we have in the
primary world. They made decisions on the basis of things like: "And it is
not our part here to take thought only for a season, or for a few lives of
Men, or for a passing age of the world. We should seek a final end of this
menace, even if we don't hope to make one.' That decision is based on a
level of certainty that would not be available to mortal Men. So in what
sense is it not 'magic'?