Believe it or not, Steve Jobs cares what’s on the cover of TIME magazine. He once called the managing editor at home in the middle of a Sunday night to demand that the website of the Canadian edition remove the cover image of the Jan. 14, 2002 issue — the one showing a flat-screen iMac — until Jobs could unveil the machine at Macworld the next morning.

So it’s probably a matter of no small interest to Apple’s (AAPL) CEO that it’s his scruffy face on the cover of the issue that hits newsstands Friday morning. (Newsweek, which put Apple on the cover last week, had to settle for a photo of a cloud.)

Jobs has now been on TIME’s cover seven times, each of them — except perhaps the May 14, 2007 issue — the product of long painful negotiations between egos used to getting their own way.

This cover package features an iPad review by Lev Grossman and a charming Jobs profile by Stephen Fry that includes this admission:

I have met five British Prime Ministers, two American Presidents, Nelson Mandela, Michael Jackson and the Queen. My hour with Steve Jobs certainly made me more nervous than any of those encounters.

Fry’s punchline: He forgets to turn on his tape recorder before he poses his first question and can’t remember what he asked or much of what Jobs answered.

See also:

• The six previous TIME cover images
• 89 Steve Jobs magazine covers
• Steve Jobs makes Time’s ‘most influential’ list
• Steve Jobs: Not Time Magazine’s Person of the Year for 2009

[Follow Philip Elmer-DeWitt on Twitter @philiped]