Brian Little was hoping to bring the 21-year-old back after he scored four goals in five loan appearances earlier in the season, but the offer has been turned down.
The Mackems do not feel that he's ready for first team football yet after suffering from a hamstring injury.
Chairman Adam Pearson said: "We were very hopeful of signing Reddy but because of a hamstring injury, he's only played something like 70 minutes football since returning to Sunderland from his first loan spell with us.
"It might have been different had he played for Sunderland's reserves on Monday night but the game was called off because of the bad weather. In the circumstances, Sunderland feel he's better off staying with them and getting a few reserve team games under his belt.
"It's disappointing but you can understand the situation. The last thing Sunderland want is their player rejoining us and then suffering a recurrence of what was a pretty serious injury before they had a chance to assess his fitness."
Neil Roberts recently returned to Wigan after spending the month as cover at Boothferry Park, but with Rodney Rowe back to fitness the club have decided not to extend the deal.
However, if the right player becomes available then City will make a move.
Pearson said: "There is a chance we might look at another loan signing although it depends what Brian [Little] wants to do."