Jerome has often been praised by McLeish for his work-rate, pace and power and was City's leading scorer last season with 11 goals.
McLeish believes he only needs to add a greater composure in front of goal to become the complete striker.
But the Blues boss accepts it would be hard for the Midlands club to then retain the services of the former England Under-21 striker who has just recovered from an ankle problem.
McLeish, whose side entertain West Ham on Saturday, said: "It is great to have Cameron back. He is a powerhouse, he has got a lot in his locker.
"But he can still can improve the final thing, the finishing. I think Cameron should be one five goals now this season with the chances he has had.
"He had one against Everton in front of goal, one up at Bolton when they got back to 2-2. He is very capable of scoring goals.
"It is just about working on trying to have ice in the head in the final third (a cool head) as Ian Wright used to say rather than just tightening up a bit."
McLeish admitted: "If he goes to that level, we will probably not be able to keep him.
"I would think a bigger club would want him, a guy with pace and power.
"If he gets his finishing up to a level, he will be a guy who would go to a higher level.
He did well at Cardiff to get to this level. Now can he go to the next level is the challenge."
McLeish knows his side have to start taking their chances after tightening up defensively with successive clean sheets against Blackpool and Aston Villa in collecting four points.
He said: "I've never really doubted our ability to defend. I think we have lost some silly goals this season which is unlike us.
"There have been some self inflicted things which have been unlike us like three own goals.
"From our point of view we've lost too many goals but I still think we've got a good ability to defend as a team.
"The main thing for us is to start burying the chances at the other end.
"It's about having that wee feel for the final moment in the box, that little bit of subtlety, class and confidence that makes the difference."
McLeish will take nothing for granted against West Ham even though they are currently bottom of the table.
He said: "The perspective people have when teams are bottom of the table is 'you should beat them, they are bottom'.
"Say, for instance, Manchester United were having a stinker of the season and had loads of injuries and they were bottom. People would still expect you to beat them because they are bottom.
"But, of course, we know that doesn't follow and anything we get against West Ham we will have to work extremely hard for because they have got some good individuals.
"They are maybe lacking a bit of confidence but, if they are, we have to capitalise."
McLeish will hand a late fitness test to key defender Roger Johnson who suffered an ankle injury against Villa.
But he is mindful of not risking the centre-back if it means he would then face a lengthy absence.
McLeish said: "He took a big responsibility in staying on at Villa but he did it and he handled it well. At that particular stage of a game, you've got to be able to trust an individual.
"But we will be able to see in the fitness test whether he is capable or not, with his mobility, and be very thorough.
"He has had a scan on his ankle and an injection as well.
"He has not missed a Premier League game. He is an ever present. He turns up for his work every week, a fantastic character.
"The key to this is if we play him, whether it then jeopardises him for a month or two months because he is a vital component of the squad."