The news is sure to alert a string of clubs, including Carlisle United, who sold him to Town for £300,000 last summer.
VIDEO: David Wagner hails Huddersfield Town supporters
The 20-year-old made 24 appearances, half of them starts, last season, having played 51 times for Carlisle.
But the Whitehaven-born player who also shone at rugby league as a youth has yet to feature this time around.
The recruitment of Croatian Ivan Paurevic from Russian club FC Ufa and Australian international Aaron Mooy on loan from Manchester City has added to the competition Dempsey already faced in the form of Jonathan Hogg, Dean Whitehead and the highly-rated Philip Billing.
Town boss David Wagner tested Dempsey in a number of positions during the 2015/16 campaign.
“We came to the conclusion Kyle is a midfielder,” he explained.
“Obviously we have very strong competition in that area.
“I have spoken with Kyle and he knows he has to keep working hard in training.
“In football, you never know when you might be needed, and players have to be ready.
“I also understand players need time on the pitch, and that if they don’t see that happening in the near future, a loan may be an option.
“We have two important matches (at home to Barnsley on Saturday and Wolves seven days later) before the deadline (on August 31).
“After those two games, we will review the situation and Kyle and I will have a talk.”
Town already have four players out on loan after left-back Jason Davidson this week joined Dutch side Groningen for the season with the possibility of a permanent switch.
Both centre-back William Boyle and striker Flo Bojaj are with former Town manager Lee Clark at Kilmarnock.
Boyle has started five of the Scottish club’s six games so far, including both Premiership games, a 2-1 home defeat by Motherwell and 2-1 victory at Hamilton Academical.
The 20-year-old scored his first career goal in the 2-1 League Cup victory at Clyde.
Bojaj, also 20, has yet to feature in the league but made one start and two appearances from the bench in the cup.
Kilmarnock make the long trip to Dingwall to face Ross County in their latest game.
Striker Jordy Hiwula, 21, has played four times (three starts) for Bradford City and scored the winner in their League I game at Peterborough United.