It is understood the 23-year-old, who played the final game of his loan spell in Monday night's 2-2 Coca-Cola Championship draw with West Brom, is due to undergo a medical on Tyneside today.
However, neither the transfer deal nor his personal terms have yet been finalised and the relevant parties remain locked in talks.
Simpson has played a major role in Newcastle's rise to the top of the Championship table, where they stand three points clear of second-placed Nottingham Forest with a game in hand.
He has made 22 appearances and his retention has been one of Hughton's main priorities this month.
Should the Magpies be able to push through a move, that would come as a boost after seeing top targets Jermaine Beckford and Matthew Kilgallon opt to stay with Leeds and Sheffield United respectively.
There were fears last week the deal might not be done after talks stalled, but there is now a new optimism on Tyneside they could get their man after all.