The 26-year-old, who is on a temporary deal at Forest from Southampton, found the net for the first time in a 3-1 win over Cardiff City on Saturday.
"I want to score as many goals as I can," the Nottingham Post quotes Sharp as saying. "I said at the start of the season that I wanted to score 20 goals and I still do, that hasn't changed.
"Any striker should be aiming to get around 20 goals. That is normally the target and it is still mine. I have only just got my first one now, but I will still try to get there."
Sharp signed for Southampton in January from Doncaster Rovers.