The 19-year-old forward's only two senior appearances this season have come in the Carabao Cup, while he has only made the bench for one Premier League fixture.
"He's a good player, there's no doubt about that," Hodgson said. "The only thing that would concern me there is that I don't know quite how many guaranteed games [he would get].
"If I was going to speak to Jurgen and he was going to talk to me about, 'I want Rhian Brewster to go out on loan and play some matches.' I'm not 100 per cent certain I could guarantee him that he would be the first name on the team sheet.
"So I'm not 100 per certain that that will do anything other than be useful for us in terms of having another player who could come in from time to time and certainly help us out.
"But if I was Jurgen Klopp and Rhian Brewster, I think I'd want to be going somewhere where I was the first name on the team sheet, and I could guarantee that between January and May I'd be playing 20 matches."