The 17-year-old came off the bench to score a superb winner for Wales in their 1-0 World Cup qualifying victory over Austria in Cardiff on Saturday just four minutes into his senior international debut.
Victory ensured Wales remained unbeaten in qualifying and four points adrift of Group D leaders Serbia.
Woodburn was born in Chester, northwest England but qualifies for Wales through his maternal grandfather.
In November, he became the youngest goal-scorer in Liverpool’s history when he was on target against Leeds United in the League Cup.
That goal alone led to renewed speculation that England would try to take Woodburn, who had been offered an Under-16 call-up after previously attending a schoolboys training camp, into their senior squad.
But Rush, who worked with Woodburn in Wales’s youth squads, was confident a change of allegiance was never on the cards.
“I know England were after him for a couple of years but he is so passionate about being Welsh,” Rush told BBC Radio on Sunday. “Chris Coleman (the Wales manager) gave him a chance and he came up trumps.
“I’ve been working with Ben since he was 14 years old and he has an amazing attitude, he keeps his feet on the ground,” added Rush, the all-time record goal-scorer for both Liverpool and Wales.
“Playing with the likes of Aaron Ramsey and Gareth Bale I think he is now realising what the world is all about,” explained the 55-year-old Rush, a key member of the successful Liverpool sides of the 1980s.
“Jurgen Klopp (the Liverpool manager) has been absolutely fantastic with him (telling him) ‘not too much too soon’, ‘be patient and your time will come and then you have to take your chance’.
“He has taken his chance but he has to be patient again because things don’t happen overnight and he must realise he probably won’t start on Tuesday (against Moldova) but if he comes on he will do a job.”