Woodley, a former UFC welterweight champion, suffered a split decision loss to the youngest Paul sibling in their tussle in August.
The reason for Fury’s rumoured withdrawal is not yet known and there has been no official confirmation despite the uncertainty.
Tommy Fury has reportedly been forced to withdraw from his grudge match with Jake Paul
Paul has been embroiled in a fierce war of words with Fury in the build-up to the showdown
Both social media sensations were due to step into the ring in Tampa, Florida.
Adding to the chaos, The Sun have also claimed that Fury’s participation is in doubt.
Fury, the half-brother of heavyweight champion Tyson, has been forced to train in his camp while coping with a cold.
‘Tommy had a little bit of a cold but hopefully he is going to be okay,’ promoter Frank Warren revealed recently.
Social media sensations Fury (left) and Paul (right) had been set to tussle in Tampa, Florida
Ahead of the fight, the youngest Paul sibling raised doubts over Fury making it to fight night
‘We are up in Morecambe [on Wednesday] so hopefully we will know more then, but he is up for it and he wants to fight.
‘He can’t wait for the fight and I know certainly from Jake’s perspective he can’t wait for the fight.’
Fury was scheduled to jet out to Florida this week to work with coach SugarHill Steward, having been trained instead by Tyson after the fight was pencilled in.
Paul, meanwhile, has held suspicions that his opponent wouldn’t make it to the fight.
The partner of Love Island star Molly-Mae Hague (right), Fury has entered the world of boxing
Fury has been training with his half-brother Tyson, the heavyweight champion of the world
On social media, Tyson has shared several updates from his time preparing Fury to fight Paul
During their feisty press conference, he told Fury: ‘Make sure you show up. Just make sure you show up.’
The pre-fight verbal slinging match descended into chaos, live on BT Sport, after Fury’s father, John, delivered a stinging comment about Paul and his girlfriend.
The broadcaster livestreamed the event, which saw Fury and Paul exchanged words. The former was joined by John, Tyson and Warren.
Paul, 24, participated via video link from Puerto Rico and traded insults with John across the farcical 22-minute event.
BT Sport issued an apology for ‘unacceptable’ remarks made during the press conference
He branded John a ‘nobody’ and told him to ‘suck my d***’ with tempers flaring.
But Fury Sr hit back in grizzly fashion by telling Paul he ‘doesn’t have a d*** to suck’, and then said: ‘You know when Tommy knocks you out, he’s gonna bend your girlfriend over and do her like a dog.’
In the aftermath, BT Sport issued a statement apologising for ‘unacceptable comments’ made during the stream.
‘This week BT Sport streamed a live boxing press conference that included a number of offensive and unacceptable comments, some of which has led to further online abuse,’ the statement read.
Fury’s father John made a vulgar comment about Paul’s girlfriend during the press conference
Fury Sr said Fury will ‘do’ Paul’s girlfriend Julia Rose after their fight if he wins by knockout
‘This goes against all the values that BT Sport wants to uphold. We would like to apologise for any offence or upset this has caused.’
Paul holds a 4-0 professional record, three of which ended by way of a knockout.
Meanwhile, Fury has fought seven times and remains unbeaten. Four of his victories came by knockout.