Nakata scored his first goal for the club - a superb free-kick - following his loan move from Fiorentina in the 2-0 defeat of West Brom.
The Japan midfielder followed up his fine display against Besiktas in the UEFA Cup in midweek with another classy performance.
Allardyce said: "We are hoping to make it a permanent deal. It is something we will look at the early in the transfer window.
"If he continues like this he will be a good capture for us.
"There were good performances from Nakata in the Confederations Cup in the summer and the price was right.
"He was determined to play in the Premiership and because he has been in Europe for so long the adjustment is easier for him than others.
"He has done a massive job in Italy the past six or seven years and I hope he can do the same for us."
Nakata made the breakthrough for Bolton in the 81st minute, firing home a free-kick from 20 yards after he was bundled over by Martin Albrechtsen.
The goal came after they had dominated the game for long spells without making their possession pay.
Allardyce said: "Nakata's overall play is beginning to get better and better. We were a little concerned as he played on Thursday as well.
"He is not that used to the Premiership but he took up the challenge and produced his quality.
"He looked more than capable of coping against a West Brom side with its tails up after beating Arsenal."