Having caught the eye at Celta, and with Spain's youth teams, it was inevitable that Europe's big guns would eventually come calling.
They did so in the winter of 2020, when Premier League clubs were keen to move before new Brexit rules, which would make it more complicated to recruit promising young overseas talent, came into force.
Manchester United and Chelsea were among those who made pitches to Bajcetic and his family, while there was of course interest from a host of clubs in La Liga, including Valencia, Atletico Madrid and Sevilla.
Liverpool, though, won the race. The Reds paid a fee of €250,000 (£220k/$243k) to land him, and he moved to Merseyside in February 2021.
"The family were convinced that Liverpool is a club that looks after young men really well," Otero told The Athletic last year. "Other big clubs in Spain wanted him but they chose Liverpool for the academy system. We hoped he could be an elite player for Celta, but we understand the proposal came and Celta cannot be at that level."
Bajcetic started out in Liverpool's U16 team, but by the end of the 2020-21 season he was a fixture in Marc Bridge-Wilkinson's U18 side, playing mainly as a central defender.
"It was difficult to leave all my friends, my family and the place I was living for all my life," he told liverpoolfc.com in the summer. But I love the football here and it's my dream."
It was in the following season, 2021-22, that the whispers started. "We've signed a gem," one Liverpool academy source told NXGN early in that campaign. Bajcetic was impressing on a weekly basis by that point, either in defence or at the base of midfield.
He appeared in the UEFA Youth League against the likes of Atletico Madrid, AC Milan and Porto, and by November 2021, just a few weeks after his 17th birthday, he had been invited to train with Liverpool's first-team.
It was there that he caught the eye of Klopp and his staff. Pep Lijnders remembers being struck by the youngster's poise and calmness.
"Jurgen immediately said he could reach the No.6 for us," Lijnders wrote in his book, Intensity. "I was so happy because we’d searched for a while for a talented No.6.
"Hopefully he could fill this position one day, but he was the surprise of [that] international break. You only get seven seconds to make a first impression on whether people feel positively or negatively about you, but as a footballer it’s probably 70 minutes, so it was definitely a case of ‘Well done, Stefan!’"