He attracted interest from a number of clubs before impressing during a trial at Loftus Road.
"I like him and definitely want to do something. I'd like to come to an agreement and take him on board," said QPR manager Neil Warnock.
Hewitt had spells with Ilford and Clapton prior to joining Harrow Borough last summer, since which he has been monitored by several Championship and League One sides.
More recently he came to QPR's attention, and this week scored twice for their reserve team in a match against Crystal Palace.
Warnock added: "I've managed in non-league, and I don't want to rip them (Harrow Borough) off. They've made him the player he is."
Source: BBC Sport
Source: BBC Sport