Woods was at Dragons training on Saturday morning, 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.
The development comes after weeks of a tug-of-war between the two clubs for Fifita and fellow uncapped Manly prop Alec Tuitavake.
The Dragons had been told that Fifita and Tuitavake were free to speak to other clubs, despite being under contract at the Sea Eagles.
The pair had agreed to terms to join the Dragons, only for Manly to ultimately agree to release Tuitavake, but not Fifita after the 22-year-old starred in the pre-season for the Sea Eagles.
Woods' name was only entered into the fray in recent days, but the Dragons are happy to release him in order to secure the young talent.
Manly are also keen to sign the former NSW and Australian Test star, with negotiations made easier by the fact Woods and Sea Eagles coach Anthony Seibold share the same manager in Isaac Moses.
A deal is close to sorted between Woods and Manly, and once that is complete, paperwork is expected to be signed off on by both clubs early in the week.
The 32-year-old Woods has not been picked in NRL this year at the Dragons, and is expected to still act as 18th man in the club's clash with Cronulla on Sunday.
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.
Dragons coach Anthony Griffin said he was hopeful of having both Tuitavake and Fifita at the club this year on Saturday morning.
"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."
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