De Laurentiis was responding to an interview that Osimhen, who is with Nigeria at the Africa Cup of Nations, gave to American television network CBS, in which the striker said he had already "made up" his mind about his next move.
Questioned by Italian media after a meeting of the Italian Football League, De Laurentiis said he was not surprised, even though Osimhen signed a contract extension with the Italian champions in December.
Italian media have reported that the contract contains a release clause of between 120 and 130 million euros (£102m to £111m).
Osimhen was the top scorer in Serie A last season, hitting 26 goals to propel Napoli to their first league title since 1990.
De Laurentiis said he had been preparing for Osimhen to leave ever since.
"We've known all this since last summer, which is also why negotiations for the extension of his contract, although friendly, took so long," De Laurentiis said.
"We know he's either going to Real Madrid, Paris Saint-Germain or an English club."
Osimhen, voted African Player of the Year last year, joined Napoli from Lille in 2020 and has scored 67 goals in 119 appearances in all competitions.
Napoli are experiencing a nightmare season. They are ninth in the league and out of the Italian Cup.
Coach Luciano Spalletti left after the title win and De Laurentiis appointed Rudi Garcia, but dismissed the Frenchman in mid-November and hired Walter Mazzarri until the end of the season.
De Laurentiis dismissed hiring Jose Mourinho as a future coach.
Mourinho is without a club after Roma terminated his contract in mid-January.
"Mourinho at Napoli is not on the agenda," De Laurentiis said.
"He's a great coach, very likeable, part of the history of a certain kind of soccer.
"His destiny will undoubtedly take him out of Italy, at least not to Naples." De Laurentiis concluded.
