The Magpies stopper currently finds himself in the spotlight after playing a key role in England's Under-20 World Cup triumph, with the youngster saving a penalty in the final against Venezuela.
Woodman remains tipped for big things at St James' Park but he is currently down the pecking order, and is expected to spend another season out on loan.
According to The Chronicle, Peterborough United, Northampton Town and Bury are all keen to secure his services for the upcoming campaign, while Kilmarnock also hold an interest in taking the 20-year-old back to Scotland.
During the second half of last season, Woodman made 15 starts for the top-flight side in all competitions, and a return to Rugby Park may appeal to him.
Despite previous call-ups to the first-team squad at Newcastle, he is yet to make a senior appearance.