The 20-year-old has just returned to the United Kingdom after playing a starring role for England Under-20s as they won the Under-20 World Cup in South Korea.
Woodman saved a penalty during the second half of the final with Venezuela, and he is expected to attract plenty of interest during the summer transfer window.
However, according to the Daily Record, a return to Kilmarnock is a strong possibility after his stint at Rugby Park this season.
After moving to Scotland in January, Woodman made 15 appearances in all competitions and would likely command a regular starting role should he pen another deal with the top-flight side.
He remains down the pecking order at St James' Park and with Rafael Benitez looking at signing another goalkeeper, he will be loaned out ahead of next season.