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The 61-year-old former Chelsea coach's contract expires at the end of the tournament in Gabon.
"I came for two years in Ghana, we extended to two years and three months because we qualified for the Nations Cup," Grant told BBC Sport.
"I will always take good memories from here, but hopefully the last memory will be the best one."
Leading Ghana to the title in Gabon, and ending the Black Stars' 35-year wait to win the Nations Cup for a fifth time, would be a sensational way for Grant to sign off.
And it would help to ease the pain of losing on penalties to Ivory Coast in the final two years ago.
Grant's side are on track in Gabon and will book a quarter-finals place if they beat Mali in their second Group D match on Saturday, having defeated Uganda 1-0 in their opener.
Regardless of whether Ghana go all the way or contrive to fail to qualify from their group, Grant's comments appear to confirm he will soon be employed elsewhere.
Grant has been linked with job offers from China and Australia, but when asked what his next move will be Grant was non-committal.
He said: "I am happy with what I have achieved in my career.  In my life I never plan. What will happen, will happen. Let's see.
"I am looking forward myself to see what will happen."
Avram Grant has given a strong indication his time as Ghana coach will end after the Africa Cup of Nations.