The Bhoys are looking to add during the winter window and have made the acquisition of a new striker a top priority.
Lennon has, however, been quick to point out that he will have to spend big if he is to get a proven marksman on board.
Goal-getters do not come cheap but, with the club having offloaded Gary Hooper to Norwich City over the summer, Mjallby feels the Celtic board need to speculate to accumulate.
He told the Daily Record: "We have worked hard and been quite successful at developing players. Sometimes, though, you just need experience.
"In an ideal world, you'll have a mix of young, hungry players and experience as well.
"I don't think it's too much to ask to maybe get a striker who might cost £5million. You are always a bit wary, though. Is he going to be worth £5million?
"The important thing is that they need to improve the team. We have been missing a player like Gary Hooper this season.
"They are hard to come by. That's just the way it is. It's not like we're in desperate need to get someone right now but we're always looking to get better and freshen things up."