He has subsequently missed three matches across all competitions against Kocaelispor, Trabzonspor and Sporting Lisbon.
Club chief medical officer Yener İnce confirmed that the Super Eagles striker will undergo further medical tests, with a final decision on his availability to be made once the results are known.
“We will conduct tests on all three players, on Osimhen, on Singo, and on Sallai as well.
“We will make a decision based on the test results,” İnce said.
“But the treatment of all three is going very well. In other words, all three are in a much better condition now compared to one week to 10 days ago.”
The Nigerian forward has resumed training and is progressing well in his rehabilitation.
Galatasaray host Kasımpaşa in the Süper Lig this weekend, with the Champions League clash against Barcelona following just a few days later at Rams Park.
Osimhen scored six goals and provided two assists in his first four league appearances this season before the injury.
A carefully managed return against Kasımpaşa could allow the club to assess his match fitness ahead of the high-profile European encounter with Barcelona.