The Hammers forward was a key figure during Allardyce’s tenure as West Ham boss, leading the line impressively when fit and helping the North Londoners to establish themselves once more.
However, following a long injury layoff, Carroll has been somewhat underused by current boss Slaven Bilic and speculation is mounting regarding a possible return to the North East.
Speaking to reporters on a potential switch to Sunderland, Allardyce has dismissed the idea and stated his belief that the former Newcastle United striker is enjoying life in the capital.
“If there are any rumours about Andy being transferred I haven't heard it and I don't think he is available,” Allardyce was quoted as saying.
“I have also heard he likes living in London. He has got his new family there and a house and he is unlikely to want to leave. He is not available as far as I am concerned.”
The 26-year-old striker has made just two Premier League starts since his return from injury, with his solitary goal coming in the 2-1 victory over Chelsea last month.
While Carroll to Sunderland is unrealistic, aside from his obvious Newcastle roots, it doesn’t hide the fact that a striker of that mould would be ideal at the Stadium of Light now.
Sunderland are desperate for goals and Allardyce may seek a powerful centre-forward in the January transfer window in order to compliment Steven Fletcher, Jermain Defoe and Jeremain Lens in attack.