The Daily Star says City, led by director of football Txiki Begiristain, have made the improvement of their wide options a main summer priorities.
Reus, who can play on either flank and through the middle, joined Dortmund from Borussia Monchengladbach last summer on a deal that runs until 2017.
City were one of the clubs keen on Reus before he moved to German champions Dortmund.
He was put off a move to Manchester by a potential lack of first-team football and then scored against City in the Champions League in October.
Sources in Germany say Reus would have the same concerns if City come calling again.