With no sign of any new players, the Sky Blues will have to rely on the former Wolves man finding the net on a far more frequent basis than he did last season.
Eastwood showed some brilliant touches with his feet and his reading of the game is excellent and Harrison wants to get this in unison and transform Eastwood into a top goalscorer.
"Freddy is a natural goalscorer, or has proved to have been in the past, but he didn't have a particularly exciting season for himself last year," said Harrison to the CT.
"It is a challenge and we have to ask the player, what can we do, what do you think we need?
"We can start there and then have a look at some of the video clips and say what about this, what about that, and let's have an afternoon on that.
"Whether he will say, 'I have got an appointment with my financial adviser,' or whoever, like a lot of them do, I don't know, but it should be football first.
"Every player is a challenge and I have always believed that if you can inside a player's brain, you are winning".
City badly need another top goalscorer to compliment Clinton Morrison and Harrison said: "It's true because goalscorers are very hard to find these days..
"It is something in his mentality and I have always found that goal-scorers are usually people that thrive on goals and lose so much confidence without goals.
"They are a different player if they are not confident, and you know that they are not getting into goalscoring positions because they are thinking too much about things.
"Most goalscorers are instinctive players. You can guide and push and say where to go and how to go, but in the end they will go where they go to score goals.
"And if you ask a natural goal-scorer where they went when they scored, they often can't tell you.
"I had that with Maurice Johnson at Watford. He hadn't got a clue, he just put the ball in the back of the net and that was instinct.
"But when they are not scoring they start to question that instinct and start to be inhibited, and goal-scorers hate to be inhibited.
"They like an arm round them and they like a lot of love in the main, and that's my job."