The Premier League duo were first alerted to the 21-year-old during the London 2012 Olympic Games, during which he produced a fine display against Team GB.
He spent two weeks with City over the summer, but his trial was not turned into a permanent move at the time.
Shortly after Abdulrahman rejected a loan approach from Benfica, in hope of a switch to the Sky Blues, who are still believed to be interested.
Arsenal are also in the chase, and could take advantage of their rivals’ stalling.
Manager Arsene Wenger has reportedly received glowing scouting reports on the youngster, and is evaluating a potential summer move.
A number of other European clubs are also said to be in the hunt, with Abdulrahman widely regarded as the finest talent from the Middle East.
As well as his playing ability, the midfielder, who currently plays for Al Ain, would serve to increase Arsenal or City’s presence in the region, which could be vital in securing sponsorship deals.
Abdulrahman has averaged almost a goal every other game at domestic level, and has also made 16 appearances for the UAE.