The 22-year-old has experience in Scotland with Aberdeen and Kilmarnock, but has played just four times for Newcastle - all in cup matches.
While he has been named in the Magpies' matchday squad on numerous occasions, Woodman - who made 23 appearances in total for the Dons and Killie - has not been able to establish himself in the first team, and is keen to leave for regular game time, according to reports.
Two English Championship sides are understood to be keen on taking Woodman on loan this season, but with the 'keeper's contract with Newcastle up next June, he is likely to consider his options with "solid interest" from Arsenal and Celtic.
Celtic's first-team goalkeepers are Scott Bain and Craig Gordon, with the former the No.1 option. Veteran shot-stopper Gordon will be 38 midway through the 2020/21 season and Celtic could well be on the lookout for a new goalkeeper to challenge Bain in the near future.
According to The Chronicle, Woodman was keen to go out on loan last season but Newcastle blocked his request after he refused to sign a contract offer.