However, South African Retief Goosen held a one-shot lead after the second round of the WGC-Bridgestone Invitational on Friday, Aug 6.
Left-hander Mickelson, recovered from a double-bogey at the 14th with two birdies in the last four holes to be snapping at Goosen's heels.
Most eyes will follow Mickelson's fortunes over the time as he bids to knock Woods from his top-ranked perch.
Victory here would do the trick or even a top-four finish if Woods places outside the top 37.
Mickelson said, "it would be something I would love to do, ultimately being regarded as number one according to the rankings."
"I know that I've got a great opportunity this week. I know that I'm playing well and this is my best opportunity," added Mickelson.