The full-back is on loan at the City Ground from Palace after struggling to break into the first-team following his move from Huddersfield Town last year.
A broken ankle in his first training session with Palace meant Hunt was unable to be part of their impressive campaign last season and was sent on loan to Barnsley in January.
He failed to help them stay in the Championship and returned to Palace to fight for a starting berth.
However, with Martin Kelly's arrival at Selhurst Park the 23-year-old found his chances limited so moved to Forest on a six-month loan.
Pearce has been impressed with Hunt's displays so far and revealed there had been initial conversations to try to keep him at the club for a longer spell.
"We are attempting to keep him here on a permanent basis," Pearce told the Nottingham Post. "We are speaking to his representatives and we have had a conversation with Palace, prior to the window shutting.
"There is an opportunity for us to extend his stay on a permanent basis, even before the window opens again. That is something we are working on doing.
"He is very keen to stay here, he is enjoying his football and is clearly enjoying working with us at the club. Hopefully we can get something done."
Hunt has featured in all nine of Forest's league games this season, helping them to second position in the table.
