Khedira - who won the World Cup this summer as a member of Joachim Low's Germany squad - has seen his future subject to all kinds of speculation in recent months, with both of those aforementioned clubs believed to be keen on capturing his signature to further bolster their respective squads ahead of the new Premier League campaign.
Former Stuttgart enforcer Khedira was expected to be surplus to requirements at Real Madrid under Ancelotti this year, primarily due to the fact that his current contract at the Santiago Bernabeu is due to expire in 2015 and he is yet to sign an extension.
Despite widespread expectations that the 27-year-old would depart La Liga however, Ancelotti has moved to rubbish such suggestions and insists that Khedira will stay put.
"He's not leaving, he's a Real Madrid player," the Italian was quoted by The Daily Star in the build-up to Real Madrid's UEFA SuperCup showdown with domestic rivals Sevilla in Cardiff on Tuesday night.
"He has a contract until June 30, 2015 and that's all there is to say."
Watch: The latest Arsenal transfer news
2015 deal possible?
Although Arsene Wenger's recent public quotes have raised serious questions over Arsenal's supposed interest in £25 million-rated Khedira, there is no doubt that his arrival would have provided a further boost to the Gunners' growing title credentials.
Chelsea boss Jose Mourinho's decision to sign Cesc Fabregas from Barcelona in June, meanwhile, looked to compensate for any potential issues that could have arisen from Frank Lampard's recent departure.
However, the Portuguese is believed to share a positive working relationship with Khedira having been brought to Real during Mourinho's three-year spell at the helm.
If either Arsenal or Chelsea do retain indeed retain a serious desire to recruit Khedira, then they may not have long to wait if he does indeed stay in Spain but continues to snub any talks of a new deal.
Although finances and transfer fees are largely immaterial to a club as reputable and wealthy as Real Madrid, surely even they would bristle at the possibility of such a talented and coveted individual walk away for nothing next summer.
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