The highly-rated midfielder is due to return to City later this month after completing a successful loan spell at Stromsgodset, helping them to win their first Norwegian title in 43 years.
The 22-year-old was instrumental in Stromsgodset's success and his performances have alerted a number of teams across Europe.
Ibrahim, who has been compared to Patrick Vieira in his playing style, is out of contract at City next summer and they are thought to be willing to listen to offers for him in January with the player keen to secure regular first-team football.
The likes of Arsenal, Roma, Lille, Marseille, Schalke, Bayer Leverkusen and Fenerbahce are all thought to be admirers after watching him in action this season.
The Norway Under-21 international admits he is unsure of his long-term future as he prepares for talks with City boss Manuel Pellegrini.
"I am very happy with my successful loan spell at Stromsgodset and helping them to win the title," Ibrahim told Sky Sports.
"Several clubs have been in contact, but I still don't know what's going to happen in January.
"I am back in Carrington this week and want to meet Manuel Pellegrini.
"I would love to get a chance in the first-team, get games and prove myself to the boss that I can play at the highest level from January as my loan agreement doesn't finish with Stromsgodset until December 31st.
"I've been at Manchester City since 2007, I became a supporter of the club and feel like a local boy.
"I would love to be given a chance and give everything for this special club."