Osimhen has come to the fore for Napoli this season, scoring 28 goals in 36 appearances across all competitions and helping them to win Serie A for the first time in more than three decades.
The Nigerian is in demand this summer with Manchester United, Chelsea and Paris Saint-Germain believed to be interested in signing him.
But there was serious interest in the forward in 2020 as well when he left Lille and Jurgen Klopp was keen to take him to Anfield then.
However, Napoli won the race and Costi revealed that it was down to Giuntoli why the Serie A giants managed to sign the Nigerian.
He claimed that the Napoli sporting director practically spent three days with Osimhen in a hotel room to convince him to move to the Stadio Diego Armando Maradona that summer.
Costi told Italian daily Tuttosport: “As complicated as the Osimhen transfer at Napoli was, it was his masterpiece.
“He was locked up in a hotel room in Rome for three days.
“He knew that Liverpool was on Victor. Klopp had come forward.
“But Cristian shut himself up in the hotel with Osimhen until he convinced him to accept Napoli.”
Both Giuntoli and Osimhen could be on the move this summer with the former believed to be on his way to joining Juventus.