Ernie Els will be named captain of the worldwide squad.
Woods is at $11 to win at Augusta next month, alongside Jordan Spieth, Justin Thomas and Rory McIlroy, with the quartet trailing only Dustin Johnson who is the $8 favourite.
The development first was reported by the blog Morning Read.
Els will take over the worldwide lead reins from Zimbabwean Nick Price.
Woods served as vice captain to Davis Love III at the 2016 Ryder Cup and excelled in that role. According to golfchannel.com, Woods is expected to be named USA captain on Tuesday.
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. He's reached out in those team rooms and really been a big part of helping the younger players and being alongside of them and then also helping the captain with some hard tasks and asks and X's and O's.
Bookmakers Neds have Woods at $7 to win at Bay Hill for an incredible ninth time, ahead of Day at $13.
Woods and Els are certain to inject some life into the matches, from their own relationship and history, and from the most intense moment in Presidents Cup history.
Woods hasn't won a major since the 2008 US Open, but Neds now have the resurgent 42-year-old as second favourite to don the green jacked for the fifth time. The rules then were for a player from each team to have his name placed in an envelope, and they would play sudden-death to decide the Presidents Cup. Els had to make from 6 feet to match him.
They also have battled plenty in tournaments.
Four-time major victor Els has finished runner-up to Woods seven times, including twice in the majors.
In 1998 in Thailand, Woods rallied from an eight-shot deficit in the final round and beating Els in a playoff.
The Presidents Cup has found tremendous corporate support with Italian carmaker Alfa Romeo, Citibank and Rolex, but the matches lack a competitive balance.
So, expect some type of format change to reduce the number of points from 30 and minimize the American depth, plus perhaps other tweaks for which Els has lobbied.
Woods plays at Bay Hill this week, where he is an eight-time victor.