United boss David Moyes was looking to add to his squad on transfer deadline day, but was rebuffed by both Real and Galatasary in his quest for midfield reinforcements.
"The club turned down the offer and that was it," Germany international Khedira said.
"We didn't really have the chance to discuss it. I had a longer chat with (Real manager) Carlo Ancelotti a few weeks ago and it was relatively clear to me that I'd stay at Real."
Netherlands international Sneijder has been linked with United at various junctures in his career, and Galatasaray sporting co-ordinator Bulunt Tulun revealed that the three-time European champions had made an "indirect bid" for the Dutchman's services.
"Sneijder received an indirect offer from Manchester United two weeks ago but it was not accepted," Tulun told Milliyet.
"There are several clubs that want him but just like we can't let go of (striker) Burak (Yilmaz) we also have to keep hold of Sneijder."
There was some good news for United on Monday, with close-season target Marouane Fellaini lured from Moyes' former club Everton for £27.5 million.
However, a bid for Athletic Bilbao's Ander Herrera proved fruitless, while a reported loan move for Madrid's Fabio Coentrao also failed to materialise.
Reports have since indicated that United were prepared to meet Herrera's €36m (£30.5m) release clause, but the Spanish Football Federation could not ratify a move before the deadline passed.
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