The Swedish star (below) is the talk of Europe again after his remarkable four-goal destruction of England in Stockholm, capped with the amazing overhead kick that is being compared to some of the greatest goals in the game's history.
Trapattoni was Fiorentina manager when Ibrahimovic, then of Malmo, first came onto his radar in 2000. Discussions took place with his agent, but they never quite moved on. "At my club, there was no money to buy him," said the Irish boss.
Before they could revisit the deal, Trapattoni was appointed national team manager and a year later Ibrahimovic joined Ajax, the first major step in a career which has taken him to Italy, Spain and now France.
The enigmatic frontman caused Trapattoni serious pain in Euro 2004, when his late backheel secured a point for Sweden that ultimately led to Italy's exit and the manager's dismissal; the 73-year-old recalled the painful memory, believing that the goalscorer committed a foul while doing so.
He is aware that, next March, the Paris Saint-Germain star is capable of orchestrating a plan that could put the boss in serious difficulty again.
"I hope he has run out of petrol," he joked, again. "I know him very well from Milan. And I managed against Sweden when he made a great foul against our goalkeeper and score a goal.
"He has experience, he has played in many countries and he is a difficult player.
"We cannot only think about him. Yes, he scores fantastic goals, but Sweden are a good team. They are strong, with technical quality, and a lot of their players are involved in the top leagues. Ibrahimovic scores goals, but we have defenders, good centre-backs."
The veteran made passing reference to Celtic's Champions League win over Barcelona before moving onto experience from his own playing days, stressing that no team should ever be overawed by one individual.
"I played against great players, like Pele, like Eusebio, like Cruyff. They were the big stars of the game and while they might have played in different ways to Ibrahimovic, I was not afraid. I might have been a little player, but I won the game and our team needs to think like this.
"They should never renounce what is possible to be achieved.
"Football is about living in the moment, and March is four months away. Many things can happen between now and then, there are a lot of games in the Champions League and a team could be missing one important player."
In other words, he is not ruling out the possibility that Ibrahimovic could pick up an injury between now and March 22.
It would take a serious problem to keep the 31-year-old away. He has come under fire in Sweden at times during his career and even temporarily retired from the fold. However, he has enjoyed a strong relationship with current boss Erik Hamren and is extremely focused on a swansong in Brazil in 2014.
Trapattoni must devise a plan to prevent that dream from coming true.