On 11 October 2010, Demirci signed a three-year professional contract with Beşiktaş.
Ibrahim Toraman said, "He is a very young and talented football player. We already know his talents. But Mami is weak. It is necessary that he gains strength to be able to play on a regular basis. Now, football is a game based on more power."
Necip Uysal added, "He must strengthen his muscles. To do this extra work, time and patience is needed." In the 2010–2011 season Muhammed opted for the number 80, also worn by Ronaldinho who wore the number while playing for Milan. He also chose the number 80 because when he made his Super Lig debut on 1 April 2012 against Samsunspor, he entered the pitch in the 80th minute as a substitute for Veli Kavlak. At the end of the match he said: "The first match got very excited to play. When the coach decided to use me made me happy. Despite the loss we played a good match. We had to take risks after we were behind. We are sorry for the defeat." He scored his first goal on 24 July 2012 against Jagiellonia Białystok in a preparation match that ended 1–1.