West Ham face Sheffield Wednesday in the third round today, and the former Bolton boss is likely to make several changes to his side.
Allardyce has said that he cannot afford to make a real challenge in the cup as promotion from the Championship is his main priority.
"These days, as a manager, you have to put your hopes to one side sometimes," said Allardyce.
"There is no doubt that Gary's top aim is to win promotion from League One, as it is with me in the Championship.
"I would be surprised if he doesn't make changes and I certainly will."
Allardyce led Bolton to the FA Cup semi-finals in 2000, losing to Aston Villa on penalties.