After Hodgson stepped down following England's elimination by Iceland at Euro 2016, Allardyce was named England manager in July, reports Xinhua.
Allardyce begins his term with a 2018 World Cup qualifying match against Slovakia on September 4 and will name his first squad soon.
Terry, with 78 caps, signed a new one-year contract with Chelsea in May and has played as captain under new manager Antonio Conte. The 35-year-old Terry retired from England duty in September 2012.
"Maybe if I get the opportunity, I might have to give him a ring. But until I come to that selection or that process, we'll wait and see. I think it depends on what John said," said Allardyce on Monday, when asked if Terry might be in line for an England return.