Yes, some of the attempts at a theory of quantum gravity indeed are hinting at a "quantum of space" around the Planck order of magnitude.
However, theories that assume a "fixed grid" sort of arrangement tend to run into issues. If space is quantized, the pattern is probably not the fixed rectangular sort, but something else instead. Perhaps the notion of space arises as a smooth approximation of some kind of graph of nodes and edges of some kind.
Source: Lee Smolin's books.
(So the search for the "quantum of space" is legit, it's just not likely to be fruitful very soon because of the scale involved. But someone's got to try it.)
However, theories that assume a "fixed grid" sort of arrangement tend to run into issues. If space is quantized, the pattern is probably not the fixed rectangular sort, but something else instead. Perhaps the notion of space arises as a smooth approximation of some kind of graph of nodes and edges of some kind.
Source: Lee Smolin's books.
(So the search for the "quantum of space" is legit, it's just not likely to be fruitful very soon because of the scale involved. But someone's got to try it.)