Is George Bush preparing to give himself a presidential pardon? On first hearing, the idea sounds utterly incredible and outrageous. How can the head of a state in which respect for the law remains an active part of the national DNA even contemplate such an arbitrary and shameless act of apparent lawlessness? Amnesties and pardons of this kind are the stock-in-trade of tinpot dictators, not constitutional leaders. And yet ...

A Bush pardon would be a sensational final act to the most divisive presidency in modern America. But he certainly has the power to grant it. Article 2 section 2 of the US constitution gives the president the power to grant reprieves and pardons. The US courts have traditionally interpreted this power widely, to include amnesties, conditional pardons and blanket pardons. And all presidents have used the power – Harry Truman's 1,913 pardons is the postwar record.

And these final weeks of a presidency have become, by convention, the pardoning season. Compared with Truman, Bill Clinton was a light pardoner. He awarded just 396 of them in his eight years as president. But as many as 218 of Clinton's pardons were issued during his final month in office in 2001 – beneficiaries included his brother Roger Clinton and his longtime Arkansas politicial ally Susan MacDougall. This settling of accounts could be the pattern which Bush is about to follow.

As of now, Bush has issued just 157 presidential pardons in nearly eight years in the White House. They have covered crimes from the manufacture of untaxed whiskey to the sale of migratory bird parts. Most of the Bush pardons involve drugs, gambling and frauds. But Bush has not issued a pardon since March 24 – when the beneficiary was a South Dakota native American called Lonnie Two Eagle who was pardoned for an assault on a reservation. But in just under seven weeks Bush's power to pardon will expire.

Not even Richard Nixon pardoned himself. It fell to his hapless successor Gerald Ford to announce, a month after Nixon's resignation in August 1974, that it was time to draw the line. Nixon had been at the centre of "an American tragedy in which we all have played a part", Ford announced in a broadcast. "It could go on and on and on, or someone must write the end to it. I have concluded that only I can do that, and if I can, I must."

But can Bush rely on Barack Obama to be so magnanimous? And can Obama be relied on to grant the wide-ranging executive pardons to the whole range of Bush administration officials that the outgoing White House may wish to protect? Maybe – but no, in the end, I don't think so either. Magnanimity is all very well when it comes to your defeated Democratic opponents. But it is a whole other ballgame when the petitioner is the outgoing president himself.

Be clear that this issue is without question in Bush's rapidly diminishing intray. Be clear too that Bush is fully prepared to protect his political allies and hitmen. He has, after all, made his own stance clear by using his powers to commute Dick Cheney's chief of staff Lewis Libby's prison sentence for obstruction of justice in the Valerie Plame affair in 2007. So, if the matter is on Bush's agenda then it is also, in some way, on Obama's too.

The possibility of a Bush pardon is not a conspiracy theorist's fantasy. It is a real and present political possibility – and Americans are beginning to wake up to it. This week, Human Rights Watch and eight other organisations including the American Civil Liberties Union, Amnesty International, and the Open Society Policy Centre, wrote a public letter urging Bush not to issue a preemptive pardon of past or present officials implicated in torture or other abuses related to the "war on terror". The groups pointed out that formal legal investigations into US torture, rendition and other abuses have so far been only patchy – a reflection of the Bush administration's determination over several years to handle detainees outside the legal process. There is a very serious possibility that dozens of cases will make their way through the US courts in the coming months and years – and it is therefore possible that hundreds of administration officials will ultimately be forced to answer for their conduct.

I do not know for certain that Bush is considering a comprehensive pre-emptive pardon for officials right through to his own Oval Office. Nor do I know for certain that the matter has been discussed with the Obama team. But common sense says these things must be taking place in some form or other. It says, moreover, that Bush and Obama may have a common interest in such an outcome. Bush wants it because it protects him and his lieutenants. Obama may want it too, because he wants a clean slate and does not want to have his presidency blighted by the legal cleaning-up operation that might ensue.

If that analysis is correct, then prepare for an unprecedented act of self-pardon by Bush that extends to dozens – perhaps hundreds – of civilian and military officials. It would be a stunning challenge to America's self-image as the upholder of law and freedom in the world. It would be a lawless outcome to a lawless war. For Bush, it would be a climactic act of the untramelled presidential authority that he and Cheney have so determinedly forged. It would send waves of outrage through America and the world. And yet, for Obama, it might nevertheless be the cleaner outcome.