Carroll has completed a permanent move to Upton Park after scoring seven goals during a loan spell last season, and Allardyce believes that the 24-year-old will establish himself back in the England side before next summer's World Cup.
The 58-year-old told The Express: "Roy will come and watch Andy and he will create the headlines for West Ham.
"It is difficult to ignore Andy scoring and creating goals when England are so short. You can't look at England and see them going to the World Cup without him.
"If he is playing and scoring goals, he could be first choice come the start of the World Cup."
The former Liverpool forward has scored two goals in nine appearances for his country.