The 20-year-old midfielder currently plays for Emirati champions Al Ain and will spend just over a week with last season's Premier League victors.
Abdulrahman arrived at Carrington on Tuesday and a decision on whether to retain the midfielder beyond the trial is expected next week.
The player confirmed the news on his Twitter feed on Monday: "Today I'll travel to Manchester for a training .. wish me good luck," before adding that it was City who he would be joining.
|7/1||Manchester City are 7/1 to win the Premier League and Champions League in 2012-13 with William Hill|
The attacking midfielder enjoyed a fine 2010-11 campaign, scoring 11 goals in 29 appearances but was limited to just seven games last term after suffering a cruciate ligament injury.
Abdulrahman's move comes after he was praised by Team GB and City defender Micah Richards who labelled the 20-year-old as a star for the future.