The Black Cats had, allegedly, arranged to sign Moses, but Poyet deemed that the winger would not be a worthwhile addition.
As a result, Moses was allowed to join Stoke City on loan and Sunderland decided to look elsewhere.
The news of Poyet's rejection of Moses follows on from yesterday's reports which suggested he also turned down the opportunity to sign Micah Richards from Manchester City – per the Daily Mail.
Would Moses have improved Sunderland?
The Nigeria international has impressed at Stoke City, a side putting together an eye-catching campaign, and it is hard to think that he wouldn't have helped Sunderland pose more of a threat.
Moses has scored four times in 22 appearances for Stoke and has become one of their main attacking influences over the season.
Sunderland, meanwhile, have struggled in offensive situations this campaign, with their lack of pace out wide a particular problem.
The Black Cats have been forced to utilise players out of position in wide areas and, as a result, it is surprising that Poyet rejected Moses.
It is true that Sunderland spent most of this summer chasing Fabio Borini from Liverpool, but the Italian never seemed likely to make the move and allowing Moses to go elsewhere seems like an oversight from the Uruguayan.
It may not have been the major reason behind his sacking, but it was a contributing factor and Poyet will likely be regretting this decision as he reflects on his time at the Stadium of Light.