The 2014 World Cup winner was one of the world's top midfielders who won almost all of football's top prizes during his time with Stuttgart, Real Madrid, Juventus and Germany.
However, one opportunity that evaded him was the chance to play in England - something the now-37-year-old admits was one of his biggest dreams.
Speaking to the Drive show on talkSPORT at a FIFA Club World Cup event in the US where the expanded tournament takes place, Khedira recalled: "I had quite a few talks with Arsenal and Arsene Wenger as well.
"I spoke to him last year about that, but also Chelsea and a few other teams.
"For certain reasons, there was never an agreement but maybe it was the wrong manager, the wrong timing or permission from my club.
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"I really missed not playing in the Premier League because it was one of my biggest dreams to play in the Premier League."
Asked if he ever had talks with Manchester United, Khedira explained: "I did. I was told that the club would like to sign me but there was one manager who didn't want me."
Quizzed on which manager it was, Khedira replied: "A Dutch guy," to which Goldstein replied: "Oh, Louis van Gaal?"
Khedira then smiled and said: "You said it!"
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Van Gaal spent two years as Man United boss between the summer of 2014 and the summer of 2016, replacing David Moyes as permanent boss.
In that time he won one trophy, the FA Cup in May 2016, but made more headlines for his outspoken views on certain players.
In addition to Cristiano Ronaldo, another of Khedira's former Madrid teammates, Angel Di Maria was involved in an infamous feud with the controversial Dutchman.
While Khedira didn't get the chance to emulate either of the two in moving to Man United, he didn't do too badly for himself.
With Stuttgart, the midfielder won the Bundesliga title before joining Real Madrid in 2010 in a summer that also saw Mesut Ozil and Di Maria join the club.
During his five years with the Spanish giants, he won the LaLiga title, two Copa del Reys and the Champions League in 2014 alongside stars including Ronaldo, Gareth Bale and Karim Benzema.
It was during his time in Madrid that he also played a key role in helping Germany to World Cup glory in 2014.
Leaving Madrid for Turin in 2015, Khedira wasn't done yet as he enjoyed a trophy-laden time with Italian giants Juventus.
As well as winning five Serie A titles, he won two Coppa Italias, the Italian Super Cup and helped Juve to the Champions League final in 2017 where he was beaten by his old club Real Madrid.
His tenure in Italy saw him reunite with Ronaldo, which is a leading factor in why Khedira believes CR7 is ahead of Lionel Messi in the 'greatest of all time' debate.
He said: "From my point of view, it's Cristiano. It's not a disrespect against Messi because what he has achieved and is still doing, especially in the U.S. is amazing.
"But I know Cristiano; I played with him for seven years in Madrid and Juventus. I know him personally quite well, so I'm 100 per cent team Ronaldo, but with all due respect to Messi."
Khedira was speaking to talkSPORT ahead of the Club World Cup in the USA, which kicks off on Sunday June 15