The 25-year-old had been a target for Premier League Chelsea before the English transfer window closed on Friday and also Saudi club Al-Ahli – but he looks set to move to Istanbul instead.
Osimhen has scored 76 goals in 133 games for Napoli and played a key role in their 2022-23 Serie A title win with 26 goals.
But he failed to maintain the explosive form that made him one of the most coveted strikers in Europe, scoring 15 times in Serie A last season.
Antonio Conte’s Napoli signed Chelsea and Belgium striker Romelu Lukaku, 31, for £30m last week.
A message from Galatasaray on social media read: “Official negotiations have begun with the football player and his club SSCN Napoli SPA regarding the temporary transfer of professional footballer Victor James Osimhen.”
Former Chelsea and Arsenal winger Willian, who left Fulham in the summer, has joined Olympiakos as a free agent.
The 36-year-old Brazilian left the Cottagers when his contract expired in the summer and has now completed a move to the Super League table toppers in Greece.
Olympiakos owner Evangelos Marinakis, who also owns Nottingham Forest, was seen with Willian watching Chelsea’s 1-1 draw with Crystal Palace at Stamford Bridge.
Willian made 67 appearances, scoring 10 goals, for Fulham in the past two seasons after joining from Brazilian side Corinthians in 2022.
He spent seven years with Chelsea between 2013 and 2020, winning five major honours – including two Premier League titles, FA Cup, EFL Cup and the Uefa Europa League – before joining Arsenal, where he spent a disappointing season.
Willian said he believes he will be able to play until he is 40.