European leaders have stayed away from the tournament's group matches held in Ukraine in protest at the jailing of former prime minister Yulia Tymoshenko, but could find themselves facing a dilemma if their teams progress.
Asked if any ministers would attend England's match against Italy in Kiev on Sunday, a spokeswoman for Cameron said: "No. They're not. It reflects ministers' busy schedules ahead of the Olympics and widespread concerns about selective justice and the rule of law in Ukraine."
The boycott has caused a headache for Ukraine which wanted to use the tournament to showcase its development as a modern democratic state, free of any Soviet hangover and ready to take its rightful place in Europe.
Tymoshenko has loomed large, however, even though she is a long way from the capital Kiev and under prison guard in hospital.
Her supporters are distributing leaflets and T-shirts to football fans across the country to draw attention to her plight and during Germany's match against the Netherlands in Kharkiv two German members of the European parliament unfurled a banner urging the release of political prisoners.
The West's view is that her trial and seven-year sentence last year - for abuse of office while prime minister - was politically motivated and smacks of "selective justice".
The Ukrainian leadership sees Western governments at fault for politicising Euro 2012.
Should England beat Italy and progress to the semi-finals they would play in the Polish capital Warsaw.
"If they make it and obviously we hope they do, and that game would not be in the Ukraine, then we would expect a minister to go," Cameron's spokeswoman said.
She declined to comment on what would happen if England should reach the final, to be played in Kiev on July 1.
England have gone out at the quarter-final stage of the 2002 and 2006 World Cups and the 2004 European Championship, but there is a feeling it might be different this time.
German leader Angela Merkel, an avid supporter of Germany's team, has so far stayed away from matches in Ukraine but will watch the Germans play Greece in Gdansk on Friday.
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