The 20-year old Ghanaian midfielder is likely to be sent out again by City to further his development after a second spell with Norwegian club Stromsgodset recently and it is believed that the Hoops are keen on his services.
Abu, who has also had a spell with Eintracht Frankfurt, played at senior level for Ghana last year and could be on his way to a club in Holland, Spain or Scotland next term.
"I am sad to leave Stromsgodset but I am leaving with a good feeling because we are top of the league and playing great football," he said.
"I am now returning to Manchester and they want me to play in a stronger league to speed up my development.
"There have been Dutch teams watching me in the stands and Spanish and Scottish teams are also interested."