Woods' recent strong form could see him qualify for the 12-man USA team, becoming the first playing captain in the event's history.
Woods and South Africa's Els are due to be announced as captains on Tuesday at the Arnold Palmer Invitational at Florida's Bay Hill.
Only Dustin Johnson is rated a better chance to win next month's Masters following Woods' fine performance at the Valspar Championship, with Woods rated at 12-1 chance by bookmakers.
Els, a four-time major champion, will follow three stints by Nick Price as captain of the Internationals.
On the heels of yet another positive step in Tiger's latest comeback, the Associated Press reported on Monday morning that Woods will be named the captain of the 2019 Presidents Cup in Australia, the bi-annual competition that features golfers from the United States taking on a team of global players ... excluding those from countries in Europe, of course, which is saved for the Ryder Cup. After it became too dark to continue play, with the pair still tied after three playoff holes, team captains Jack Nicklaus and Gary Player agreed to end the event in a tie.
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The two players infamously went head-to-head in a play-off in the 2003 Presidents Cup after the match ended in a 17-17 tie.
Woods has been heavily involved in team event while not playing in recent years because of back injuries.
It will be Woods first taste of U.S. team captaincy after being a 2016 Hazeltine Ryder Cup vice-captain and also a vice-captain under Stricker at last year's Presidents Cup.
The President's Cup has been famously one-sided since its inception in 1994, with the worldwide team winning just once - at Royal Melbourne in 1998. The US has won ten, with the global team winning just once.
The Presidents Cup-Ryder Cup captaincy crossover hasn't always been the norm (Fred Couples has captained three Presidents Cups but no Ryder Cups), but the template for global golf has changed. Will he be a playing captain?