On the eve of The Barclays Scottish Open the Masters Tournament champion spent his entire press conference wiping blood away from above his right eyebrow.
Mickelson joked that he had got into "a little tiff" with another player before explaining: "I just scratched myself."
His two-week trip to Britain also sees him attempt to win The Open Championship at St Andrews on Sunday week, but finishing first or second this weekend should enable him to unseat Woods, who has held the top spot for the past five years.
Three years ago Mickelson lost a play-off to Frenchman Gregory Havret and he stated: "I always look forward to these two weeks and it would mean a lot to win here."
He insists the number one position is "not something I think about," but after more than 250 weeks just below Woods in the rankings to get there at long last will surely mean an awful lot.
When asked where it would rank amongst his achievements in the game, though, the 40 year old said he did not want to deal in hypothetical situations and would answer only on Sunday afternoon if it happens.
Mickelson's Open Championship record boasts only one top-ten finish - his third place at Royal Troon in 2004, just a stroke behind Todd Hamilton and Ernie Els - but he remembers being on the leaderboard at some stage in each of the three championships he has played at The Home of Golf.
In 1995, however, he ended up 39th, in 2000 he was 11th and five years ago he came only 60th.
Woods, of course, won those last two events by eight and five strokes respectively.
"In the three Opens I played Tiger has won (twice) and John Daly the third. Length is a factor - the further you're able to carry the ball the more bunkers you are able to eliminate.
"One of the things I've been working on in my preparation is trying to swing the club head faster. I will be swinging much harder than I would normally in a number of Open Championships where you're trying to keep the ball in a tighter fairway."