Mihajlovic had been amazed by the precocious youngster, who was giving him and his fellow first-team defenders trouble in training, as well as racking up goals for the youth team.
On March 28, 1993, with Roma winning 2-0 at Brescia, Mihajlovic ran up to Boskov and said "Come on, bring the kid on ... ". The rest is history.
Mihajlovic joked at the weekend that Totti owes him a dinner for that, and "It can't be at a pizzeria, it has to be oysters and champagne" before adding "He is the best player in Italy since I've been here".
And for nearly a quarter of a century Totti has been living up to those expectations. With his stunning goals and defence-splitting passes, Totti is, for many Roma fans, the epitome of the Roman gladiator that he has tattooed on his right shoulder.
If Rome is the Eternal City, Totti is Roma's eternal leader and has been since he was first made captain in 1998, at the age of just 22.
Zdenek Zeman, who promoted Totti to the captaincy, was such an ardent admirer that he once said: "Who are the best five Italian players? Totti, Totti, Totti, Totti, Totti."
Totti has spent his entire career at Roma and when his current contract expires, he will have had 25 years in its first team - remarkably more than 28 per cent of the club's existence.
Totti could have won more than the solitary Serie A title, two Italian Cups and two national Super Cups he lifted with Roma, but he rejected offers of more money and glory to remain with his childhood club.
"I grew up playing for Roma and I want to die playing for Roma ... I have always been a Roma fan," said Totti.
Totti's face adorns murals and posters across Italy's capital, where he is loved by Roma fans and respected by supporters of bitter rival Lazio, despite his antics against them.
Totti has scored 11 times against Lazio and often celebrates these extra-special goals with T-shirts made for the occasion.
One famously said "I have purged you again," while he revealed another reading simply "Game Over" after a victory in May 2015.
He hit the headlines in January of that year when he scored the second of two goals against Lazio and, in a pre-planned celebration for becoming the all-time leading scorer in the derby, grabbed his phone off Roma's goalkeeping coach and took a selfie under the Curva Sud with thousands of adoring fans in the background.
He grabbed global attention at Euro 2000 with one of the moments of the tournament, in the semifinals against the Netherlands.
In the tense penalty shootout, the 23-year-old Totti kept his cool to cheekily chip Edwin van der Sar with his spot-kick.
Totti played in all seven of Italy's World Cup matches in 2006 and his last match for the Azzurri was the final against France, concluding his international career with 58 caps and nine goals.
Asked what gift Totti should get for his 40th birthday, Roma coach Luciano Spalletti was among the people who suggested a time machine.
- AP
