Woods was at Dragons training on Saturday as news of the potential move broke, but his time at the NRL club is expected to end soon after failing to be picked in first grade so far this year.
AAP has been told both clubs are hopeful of completing the deal, which would bring the Dragons a rising young star and give Manly much-needed experience in their pack.
Negotiations have been put to the side for the weekend, but will likely ramp up again on Monday after weeks of discussions between the two clubs around two of Manly's young forwards.
The Dragons initially made an approach for uncapped Sea Eagles props Alec Tuitavake and Fifita, under the belief both had been given permission to look elsewhere.
Tuitavake was off contract this year while Fifita is off contract in 2024, and both impressed in Manly's pre-season challenge wins.
Tuitavake has since been granted a release by the Sea Eagles and will head to the Dragons immediately.
But the Sea Eagles were holding firm on Fifita, with coach Anthony Seibold stating earlier this year he wanted the 22-year-old to challenge for first grade in 2023.
A swap for Woods now looms as the potential solution to the impasse.
The 32-year-old Woods has become a reserve at the Dragons, after a career which has included 14 State of Origin matches for NSW and 17 Tests for Australia.
His arrival at the Sea Eagles would make them his fifth NRL club in eight years, having also played for Wests Tigers, the Bulldogs and Cronulla.
Fifita has been part of Manly's development system since the age of 14, one of several players at the Sea Eagles managed by Mario Tartak.
Speaking before news of the possible Woods swap broke, Dragons coach Anthony Griffin said he was hopeful of having both Tuitavake and Fifita at the club this year.
"It's between both club managements now. They've been speaking about the possibilities of those guys joining," Griffin said.
"I was briefed on it yesterday.
"I understand Manly having two players on contract, but as I understand it, they were given permission to negotiate. I'll leave that to the guys in suits."
13°C