There were "Gnomes", but it was just a previous name for the Noldor.
From Tolkien Gateway:
The term Gnomes or Noldoli was briefly used in J.R.R. Tolkien's early work The Book of Lost Tales to describe the race of Elves that would become the Noldor. In those works he borrowed several folkloric names to describe his original creations, like Fae, Elves, Dwarves, Ogres and Goblins.
This is also mentioned in Wikipedia.
The name was inspired by the ancient Greek "gnome" meaning thought or intelligence, and it was originally going to appear in the text of The Hobbit. From Tolkien's Letters, Letter #239 to Allen & Unwin (20 July 1962):
If gnomos is used as a translation of dwarves, then it must not appear on p. 63 in the elves that are now called Gnomes. I need not trouble the translator, or you, with the long explanation needed to account for this aberration; but the word was used as a translation of the real name, according to my mythology, of the High-elven people of the West. Pedantically, associating it with Greek gnome 'thought, intelligence'. But I have abandoned it, since it is quite impossible to dissociate the name from the popular associations of the Paracelsan gnomus = pygmaeus.1 Since this word is used – for its aptness in preference to Sp[anish] enano I am not able to judge – for 'dwarves', regrettable confusion would be caused, if it is also applied to the High Elves. I earnestly suggest that on p. 63, lines 6-7, the translator should translate old swords of the High Elves of the West; and on p. 173, line 14, should delete (or Gnomes) altogether. I think these are the only places where Gnomes appears in The Hobbit.
See Wiktionary for more detail on the meaning of the ancient Greek "gnome" (γνώμη).
Believe it or not, an early title considered for The Silmarillion was "The History of the Gnomes". Yeaaaah ... doesn't quite have the same ring to it, does it?