The reports, also carried by Portuguese newspaper A Bola, claim that United triggered the Turkey international’s £20m release clause but last minute paperwork complications killed the deal for the one-time Chelsea target.
United fell foul of the transfer deadline twice then, as their move for Real Madrid full-back Fabio Coentrao also failed to beat the clock on Monday night.
Moyes was extremely busy on the final day of the summer window, signing Marouane Fellaini from Everton. But it seems the Belgian international was not his only target, with bids for Real Madrid midfielder Sami Khedira and Ander Herrera lodged in the final hours of the window according to reports.
Turan, 26, joined the La Liga club from Galatasaray in 2011 and was also linked with a move to Chelsea this summer.
Chelsea signed Andre Schurrle and Marco van Ginkel among others during the window, which lead to a cooling of interest in Turan.
Manchester United, in contrast, were frustrated in their pursuit of midfielder reinforcements, with Cesc Fabregas another target that ultimately decided to stay put.