The 18-year-old joined the side back in August and has featured prominently in their campaign so far, making a total of 17 appearances for the Owls.
Cleethorpes Town last played on December 3rd, with Moore-Billam playing just shy of an hour in a 3-2 defeat at Dunston.
He will be in line to play in the big Boxing Day home clash against Grimsby Borough before a first game of 2023 taking the Owls away to Lincoln United.
