The 22-year-old has impressed for the Swans so far this campaign, starting 14 games out of a possible 15, keeping five clean sheets and conceding only 13 goals in the process. His performances have helped the Welsh side reach the automatic promotion spots with 28 points, one more than West Bromwich Albion.
Football Insider report that Newcastle are closely monitoring Woodman's situation at Swansea and will look to make a decision on the Englishman's future come the end of the season.
It is believed that the value of the goalkeeper will rocket to £10m by the end of the year if he continues to showcase his talent between the sticks at the south Wales club, and Newcastle may be eager to cash in on the asset given their abundance of goalkeepers already at the club.
The Tyneside club already have Martin Dúbravka as their first choice goalkeeper, and have experienced options in reserve in the form of former Charlton stopper Rob Elliot (33) and Karl Dunlow (29).
Mike Ashley may have the final say on any decision regarding Woodman, assuming he is still the owner of the club come the end of the season. With Woodman impressing Steve Cooper and receiving minutes on the pitch, the goalkeeper's value may soar if Swansea manage to achieve promotion into the Premier League.
Speaking to reports ahead of Newcastle's trip to the London Stadium to face West Ham, Bruce told reporters: "