Number 10 (British Prime Minister's Office) would not join those suggesting the football event should be cancelled, but the fact that this is being mooted by some "shows the importance of Russia changing course, before its international standing is damaged even further", a spokesman said.
"The prime minister does not believe we should reach immediately for boycotts, but it is also not surprising, given Russian behaviour, that people are starting to raise the issue," he said.
Labour's shadow foreign secretary Douglas Alexander also urged football's governing body, FIFA, to draw up contingency plans for the event to be held elsewhere.
Some German politicians have already called for the 2018 World Cup bidding contest to be re-run after international condemnation of Russia over its reaction to the crash of Malaysia Airlines flight MH17 in Ukraine.
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The Kremlin denies that any of its weapons were used to shoot down the plane but the UK, US and Ukraine have all said there are strong reasons to suspect the plane was shot down accidentally by pro-Putin separatists using a Soviet-era missile supplied by Russia.
However, Clegg told the Sunday Times that stripping Russia of major sporting events would be a "very potent political and symbolic sanction".
"Vladimir Putin himself has to understand that he can't have his cake and eat it," the Liberal Democrat leader said.
"He can't constantly push the patience of the international community beyond breaking point, destabilise a neighbouring country, protect these armed separatists in the east of Ukraine and still have the privilege and honour of receiving all the accolades in 2018 for being the host nation of the World Cup," Clegg said.
Labour's Alexander said FIFA needed to think about who else could hold the World Cup in 2018 if it is proven that Russia had responsibility for the Malaysian airliner crash.