Leeds are said to have added he should go and show them their judgment was wrong, a conversation that “stuck with" Godfrey.
Godfrey told Everton's official website: "I probably doubted myself when I was in and out of clubs - and did question whether it was for me.
"When you are younger and football is not going well, you forget about it, you are going out with friends and having fun.
"I was lucky my mindset switched at around 15 or 16.
"Something clicked - because of my own determination, not out of bitterness - and I thought; 'I'm going to prove clubs wrong and make them regret letting me go'."