Ghana beat Uganda and Mali to book passage to the quarter-finals of Gabon 2017 ahead of the mid-week encounter, while Egypt need a draw in the least to have any chance of reaching the knockout stage of the continental showpiece.
The two sides met in the 2018 World Cup qualifying group stage first round in November, with Egypt picking a famous 2-0 win in Alexandria.
“If you watched our last game with Egypt in Alexandria in the World Cup qualifiers, you will notice that we dominated the game completely," Grant said.
"Our goalkeeper [Razak Brimah] didn’t get to touch the ball most of the match, but in the end, we lost.
“This [match on Wednesday] won’t be a one-sided game; Egypt is a great team and they know how to play good football.
"I like such battles, even if it is not important on paper.
"We are on top of the group with only two goals and Egypt has one goal while the other teams didn’t score. That’s not a coincidence.”
Ghana currently sit two points clear on top of the group standings. Egypt are second with four points, while Mali and Uganda come with one and zero point respectively.
The outcome of Wednesday's game, coupled with the result of Mali's fixture with Uganda in the other group game, will determine who face Morocco and DR Congo, who both qualified from Group C.
Ghana are looking to annex the Afcon trophy for the first time since 1982.
The Black Stars finished second at the 2015 event held in Equatorial Guinea.