The surprise move comes after Davis quit as an MP and shadow home secretary to force a by-election in his constituency of Haltemprice and Howden in east Yorkshire on the issue of civil liberties and 42-day detention of terror suspects.
Davis believes the government's plans to extend detention without charge are an assault on sacred British freedoms.
At present, no party has said they will contest it, meaning Davis could be returned without a vote. The Liberal Democrats have said they support Davis's stand on 42-day detention and Labour are still considering whether to take part.
MacKenzie, who now writes a column for the Sun, revealed on Radio 4's 'Today' programme that Rupert Murdoch suggested to MacKenzie that he run against Davis.
He added that if he stood it would be with the support of Murdoch and Sun editor Rebekah Wade, because "both felt that democracy would not be best served by a walkover and suggested to me last night that I might be the person to fill the hole".
Mackenzie, who backs Labour on the 42 days issue, also told the BBC: "I have been associated with The Sun for 30 years. The Sun is very, very hostile to David Davis because of his 28 day stance and The Sun has always been very up for 42 days and perhaps even 420 days.
"I will 90% stand if Labour don't put a candidate up... I've got to get my ducks in a row, the people of what would be my new constituency would like me to have thought this thing through. Democracy has to be about two and not about one."
MacKenzie's decision to consider standing is not the first time he has dabbled in politics.
In May, MacKenzie stood unsuccessfully in a borough council election in Weybridge on the issue of parking charges.
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