The 31-year-old joined the Blacks in July and has scored two goals in cup tournament which saw them progressing to the next rounds.
"Asamoah Gyan played in two Cup matches and scored two goals that carried us on. In Fenerbahce, he came on from the bench in the last minutes of the game and did his job," Bedir told the Turkish media.
"He did not start the preseason camping with the team because he was with the national team and was not physically ready so he had a slow preparation for the season.
Bedir has also hinted that the club is willing to open up talks with Gyan in order to extend his stay.
"Gyan is a great character who is always willing to hit the summit and with his recent performance, we will talk more about Gyan in the coming weeks," he added.
Gyan pulled out of the 2018 Fifa World Cup qualifying dead rubber fixture against Egypt which ended in a 1-1 stalemate, but he is expected to join his club side on Wednesday ahead of the weekend's fixture