Poole, a regular goalscorer for City's reserve side, will go straight into the squad for Saturday's home game with Aldershot.
Shakers boss Alan Knill said: "We've watched the Man City squad quite a lot recently and they do have some really good players.
"We wanted a bit more energy in the side, he can play left or right wing or down the middle.
"He is one of those that can play all over and he's a really good footballer. We think he will just add to the squad.
"It's all about competition for places and James will give us that."