Rhodes, 21, has struck 25 goals in 21 League One appearances this season, leading to suggestions that he could leave Huddersfield in the January transfer window.
Allardyce had a £3m bid rejected for the young striker earlier in the week, and has stated that he is unlikely to submit an improved offer.
"It's something we've tried to do but it's not a situation where it looks like Huddersfield want to lose the player," Allardyce told talkSPORT.
"When a club of Huddersfield's status decide they don't want to lose him because of their own position, and it's more important that they keep him for their promotion push, then it becomes very difficult for us to prise the player away."
West Ham could move top of the Championship with victory at Portsmouth on Saturday afternoon.