The 26-year-old was injured during his nations FIFA World Cup play-off loss to the Democratic Republic of Congo, coming off at half-time due to a reported hamstring strain.
Turkish Super Lig defending champions Gala have now confirmed the results of the forwards recent medical examinations with the club.
"His MRI was performed here," said Galatasaray president Dursun Ozbek to Hurriyet.
"He'll likely have a recovery period of approximately two weeks. Our focus is on Osimhen being ready for the Fenerbahce match. Our doctors are working on that."
The news means the forward could be ready to play in the Istanbul derby on December 1 and also make him available to feature for the Super Eagles at AFCON 2025 which starts on December 21.
Nigeria will be looking to make up for their failure to qualify for the 2026 World Cup by winning their fourth AFCON title whilst improving on the AFCON 2023 final loss to Ivory Coast.
The Super Eagles will be in Group C alongside Tunisia, Tanzania and Uganda for the continental tournament next month.
Nigeria's Super Eagles have taken the first big step towards the 2025 Africa Cup of Nations (AFCON) in Morocco, with head coach Eric Chelle submitting a 55-man provisional squad.
Marcus Rashford has burst back into form at Barcelona, and coach Hansi Flick believes the key lies in the forward's bold move to a new country and way of life.
Itumeleng Khune has voiced his surprise over the exclusion of Thembinkosi Lorch from Bafana Bafana's latest AFCON squad, signalling growing concern about coach Hugo Broos' selections.
South Africa's head coach Hugo Broos has announced his 54-man preliminary squad for the 2025 African Nations Cup in Morocco that begins next month.
