The word came from French in the 13th century and always seems to have had positive associations. Savours are nice things.
Shakespeare uses it in this way, as when Sly says "I smell sweet savours"
(The Taming of the Shrew, Induction 2.70). But there are three places where the smell is definitely not nice: Salisbury in King John (IV.iii.112) talks about "Th'uncleanly savours of a slaughter-house"; Stephano sings of "the savour of tar" (The Tempest, II.ii.51); and Polixenes, appalled at the thought of seducing Hermione, asserts: "Turn then my freshest reputation to A savour that may strike the dullest nostril where I arrive" (The Winter's Tale, I.ii.421).
Savour in these cases means "stench" or "stink". And it is the negative sense which dominates, too, when Gonerill tells Lear: "This admiration ...
is much o'the savour Of other your new pranks" (King Lear, I.iv.233).
Note also the similar use of a word as a verb in Pericles (IV.vi.108), when Lysimachus describes the brothel: "The very doors and windows savour vilely".