The pair, plus 2013 Masters winner Adam Scott, are part of a newly-formed seven-person "transaction subcommittee" by the PGA Tour to hold negotiations with the Saudi Arabia-backed LIV Golf.
It comes after McIlroy, who has previously been one of the arch critics of the breakaway tour, revealed he would not replace Webb Simpson on the PGA Tour policy board after the prospect of his return reopened "old wounds" among other players.
Several outlets have reported that Woods, Patrick Cantlay and Jordan Spieth vetoed the possibility of McIlroy rejoining the board, but the Northern Irishman bears no grudges towards the 48-year-old.
He said: "I think friends can have disagreements or not see eye to eye on things.
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