The former Liverpool and England winger, 45, recently signed a two-year contract with Rovers but had previously applied for the Vale post.
He told BBC Radio Stoke: "There was truth in the rumours, but the way things worked out I ended up at Tranmere.
"I'm impressed with what Micky Adams has done throughout his career. He's been successful wherever he's gone.
"Port Vale are an ambitious club, and I wish them all the best."