Allardyce confirmed that all the elements of the switch are in place and Carroll's decision is imminent.
Big Sam told the People: "We are both out of the country but most of the negotiations are done and the financial agreement between us and Liverpool is in place.
"It's about communicating with Andy and his agent between London, here in Spain where I am and Florida where Andy is.
"I've no real need to speak to him over his decision. I've spoken to him enough times so he knows what I think and it's up to him.
"He's back in the next few days so we should have a definitive answer by the end of next week."