Highly-rated Ibrahim is currently on loan at Norwegian side Stromsgodset, but he has a clause inserted in his loan deal which allows him to leave this summer if a club makes an offer for his services.
Ibrahim is entering the final year of his contract at City and with the Norway Under-21 international well down the pecking order in Manuel Pellegrini's star-studded squad, they are ready to let him leave for free.
A host of top-flight clubs in the UK are thought to be keeping tabs on the Somalia-born player, who has been outstanding for Stromsgodset this season.
Crystal Palace, West Brom, Newcastle, Swansea, Hull and Scottish champions Celtic are all thought to be admirers of the 22-year-old after tracking his progress in the Tippeligaen.
Palace are thought to be leading the chase for Ibrahim after seeing a move for Newcastle's Dan Gosling fall through.
Ibrahim is keen to be playing regular first-team football at this stage of his career and is hoping to resolve his long-term future in the next few weeks.
"Yes, it's true the club gave me a free transfer last week and my advisors are speaking with clubs at this stage," Ibrahim told Sky Sports.
"I'm hoping to have my future sorted in the next couple of weeks hopefully by mid August.
"Stromsgodset have been really good to me and I have developed so much here, but now I would like to test myself at the highest level which is playing in the Premier League week in week out."