The new president of European soccer’s governing body settled into a chair in his glass-walled office in Switzerland, glanced out at the sweeping views of Lake Geneva and insisted he would not be there long enough to get comfortable.

It was 2017, soccer was still emerging from its greatest scandal and Aleksander Ceferin, only a few months into his presidency, was unequivocal that he was already on the clock. The sport, he said, could no longer accept leaders who grew so comfortable with the trappings of power and luxury that they worked the system to remain in their jobs. He would not be like them, he promised.

The three-year term to which he had been elected, finishing out the one vacated by his disgraced predecessor, “is already one term for me,” he said. If he was fortunate enough to earn the two more full four-year terms allowed by the rules, fine. But that would be it. Mr. Ceferin had no interest in being a president for life.

“They said: ‘Why have term limits? You can be here for 20 or 30 years,’” he said at the time. “I do not want to stay for 20 years.”

Less than a decade later, Mr. Ceferin may have had a change of heart. At his urging, the soccer body that he runs, UEFA, will vote next week on a set of rule changes that includes a measure that would allow Mr. Ceferin to stay in the presidency of one of the world’s richest sports organizations for years beyond the end date he once promised.

He is not the only leader ushered in by someone else’s scandal now seeking to strengthen his hold on a powerful job. A similar term-limits extension was already quietly approved by soccer’s global governing body, FIFA, ensuring that its president, Gianni Infantino, is eligible for an extra four-year term in a job that paid him about $4.5 million in cash and bonuses in 2022.