Reports in the local media over the weekend suggested that the Boro number two wanted to quit the Teesside outfit.
However, Crossley - who signed a two-year deal at The Riverside last summer - has stated how happy he is at The Riverside.
"Where the story came from I don't know," he told the club's official website.
"There's no way I want to leave here, it's an up and coming, growing club and I want to be part of things over the next two or three years here.
"I'm very happy here and settled and there's just no reason at all I would want to leave.
I've got 18 months left on my contract, thank God, and I'm feeling fitter now at 33 than I have all my career because of the specialised training we're getting.
"I want to play until I'm 38 or 39 and the longer you can play at the top level the better so there's no reason why I can't go on."
