The Evening Chronicle says Toon chiefs are trying to secure a League One loan swap for the highly-rated stopper to give him more experience.
England Under-20s star Woodman has been on the radar of Liverpool and Tottenham over the past few years.
And after he scooped the Golden Glove award as the Young Lions won the World Cup, his stock has risen dramatically.
The Croydon-born keeper signed a new four-year deal last summer and is happy to go out on loan.
Northampton Town and Heart of Midlothian have both expressed an interest but no terms have been agreed.