The Black Stars face the Eagles on matchday two of the continental showpiece, two years after a 1-1 deadlock in their last meeting - an international friendly match in France.
The two sides met four times at the 2012 and 2013 Afcons combined, with each side winning two.
"We know Mali is a good and very physical team, but I don't think we are a weak one either," Grant said.
"We will play on our positive points. Every team has its strength and weakness, and we have to work on that.
"We played a friendly against Mali that ended in a 1-1 draw in Paris.
"They are a good and well-organized team but we know what we want to do."
The Black Stars have been on a difficult path since their ill-campaign at the 2014 Fifa World Cup in Brazil.
The team were winless in their last five matches in all competitions prior to the Afcon, and their predicaments have not been helped by an unconvincing display against Uganda in the group opener.
The 2015 finalists have been hit with criticisms from all corners, but Grant is not getting derailed by the backlash.
He said: "I never think negative, and the people in Ghana know what the profile of their team is.
"We were not the favourites at the last Afcon [in 2015], yet we reached the final.
"We just think of winning the next game and then see what happens. We are not the only candidates.
"Even though we have lots of problems, we will show the character we've got - like we did two years ago."
Ghana's opening day 1-0 victory currently puts them on top of the table, and a win on Saturday will all but book them a ticket to the last eight.