According to 'Sky Sports', Huddersfield would like to bolster their attacking options and Roberts, who does not appear part of Pep Guardiola's plans for this season, would fit the billing.
The 21-year-old has spent the last few seasons on loan in Scotland at Celtic, winning back-to-back domestic trebles and competing in the Champions League.
Roberts travelled to the United States with the 'Citizens' for their pre-season tour, though has only made three appearances for Pep Guardiola's side since joining from Fulham in 2015.
The player has featured in the England set-up from the under-16 team to the under-20 team, and with regular football at Huddersfield could put himself in contention for a place in Gareth Southgate's team.
It is thought 'City' may prefer a permanent deal for Roberts, though a loan is not out of the question.