The Bhoys boss believes there is 'potential' in the strike force already at his disposal, but feels there is still a need to bring in added firepower.
Acquiring the 'finished article' will cost big money, something Lennon is aware of and appreciative of.
He is, however, confident that he will receive the necessary backing from his board to further strengthen a squad which lost top marksman Gary Hooper to Norwich City over the summer.
On his efforts to bring in another goal-getter, Lennon told the Daily Record: "That would be lovely. It would be helpful as well but I have players here that have the potential to improve and score at that level.
"At the moment we will work away with them and endeavour to do that.
"I don't know how much money we will have again in January but Peter Lawwell has given us assurances there will be cash to spend.
"I have four strikers I want to persevere with and work with to try to improve the goal ratio.
"In Teemu Pukki we have a player who will score. He needs a bit of time to settle to the game. But he has shown more indication now that he is getting used to playing the style of football here. I think he will be okay.
"But that area is where the big bucks are. That is where players cost money. Again, we will try to be inventive.
"If we do break the wage structure it will not be by a great deal but if we are trying to bring a type of player in we might have to push the boat out a little. We don't want to push it out too much - we are realistic with our wage structure."