Clegg, the most senior British politician to call for such action, said Putin's behaviour towards Ukraine was "beyond the pale" and had reached "a tipping point".
He spoke out as fighting around the site of MH17, the Malaysian airliner downed in eastern Ukraine on July 17, prevented a visit by international experts and as the European Union weighed new sanctions on Russia.
"If there's one thing that Vladimir Putin cares about, as far as I can see, it's his sense of status," Clegg told The Sunday Times newspaper. "Maybe reminding him that you can't retain the same status in the world if you ignore the rest of the world, maybe that will have some effect on his thinking."
The intervention by Clegg, the leader of the Liberal Democrats, the junior partner in Britain's two-party coalition, put pressure on Prime Minister David Cameron, the leader of the ruling Conservatives, to clarify his position on the matter.
A spokesperson for Cameron told Reuters the British leader was not in favour of taking the World Cup away from Russia at this stage, but signalled his position could change.
"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," the spokesperson said. "It shows the importance of Russia changing course, before its international standing is damaged even further."
Clegg said it was up to Putin to change his Ukraine policy. "He (Putin) can't constantly, you know, 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.
FIFA disagrees
Some German politicians have also called for Russia to be stripped of the right to host the tournament, but Fifa, soccer's world governing body, has so far resisted the demands, saying the competition could be "a force for good".
Almost 200 Dutch citizens lost their lives in the incident and the Dutch football association has said it will meet in due course to decide if it will take part in the qualifying competition for the finals in Russia.
Western politicians have taken an increasingly tough line on Russia since the downing of MH17, accusing Moscow of arming the separatists there, something Russia denies. Clegg said the world would look weak and insincere if it allowed Russia to stage the World Cup without a change of course by Putin in Ukraine.
"You can't have this - the beautiful game marred by the ugly aggression of Russia on the Russian-Ukrainian border," he said.
Britain's opposition Labour party also said stripping Russia of the World Cup should be an option if its complicity in the downing of MH17 was proven and if Putin did not change course.
"Fifa should be considering contingencies now and any discussion should happen quickly, so that if necessary, alternative plans are in place in time for teams and fans from around the world," Douglas Alexander, Labour's spokesman on foreign affairs, said in a statement.
Britain, which is home to many wealthy Russians, said on Saturday it thought it highly likely that MH17 was shot down from a separatist-controlled area with a missile system supplied by Moscow.
Russia's ambassador to Britain has said Moscow is only providing humanitarian aid to the separatists. He said there was no proof of his country's involvement. Clegg also said Russia should not be allowed to host a Formula One Grand Prix in October, but F1 boss Bernie Ecclestone has said that event will go ahead as planned.
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This Britain’s Deputy Prime Minister Nick Clegg should probably resign from political positions since all he can do is use Sports to push his unsubstantiated propagandized factless war mongering positions........People like this make terrorism prosper.
Russia should lose the cup over how the Olympics hosting went from what I heard.
From what I gather, anyone's of far better integrity than the chronic liar that is Nick Clegg. To even consider his 'suggestion' let alone giving in to it or his many pledges is plain foolish.