Both Allardyce and Carroll are currently abroad on holiday but the striker is expected to sign a six-year deal worth more than £15m when he returns.
The 24-year-old England international spent last season on loan with the Hammers from parent club Liverpool, who will not only lose £20m on the player they bought from Newcastle United in January 2011, but also hand him a £2m 'golden goodbye' payment because he did not request a transfer.
"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," Allardyce told the Sunday People.
"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."