Leeds are yet to publicly confirm Allardyce's appointment as their new manager and Javi Gracia's sacking, but the former England boss spoke to Jim White from the club's training ground on Wednesday morning.
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Allardyce has been out of management since 2021, but said it was an instant decision to take the job.
"I'm stood here in my office overlooking the training ground, the fabulous facilities here at Leeds, excited to be involved again," he said.
"Obviously there's a tingle that runs through your veins when you take over a football club.
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"I know it's in a lot of trouble. I've seen a lot of trouble before and hopefully - I could have done a little bit more time, but four games - hopefully we can make a difference and keep this fabulous club in the Premier League."
Asked what he thought of the opportunity, Allardyce added: "[I was] shocked, I never thought at this, at this stage of the season, there would be jobs offered.
"When the phone popped up with a name that I knew pretty well, I knew who it was straight away. So it took me about two seconds to say yes.
"Yes, Karl Robinson [joins]. And hopefully following will be another member of staff, maybe a bit more. We don't know yet, but certainly Karl at this moment in time."
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