Carroll, who is nearing the end of a season-long loan at West Ham, has not played for England since a substitute appearance in the 5-0 World Cup qualifying win over San Marino at Wembley in October.
An impressive performance in Wednesday's 2-2 draw with Manchester United has prompted calls for Carroll to be drafted back into the England fold, but Allardyce believes Hodgson is mindful of the repercussions of such a decision.
"Roy would be scared to do it because of the reaction he'd get," said Allardyce. "He would be accused of a direct approach and people would be on his case.
"But playing Andy does not make you a long-ball team, it just gives you extra options. He is good on the floor and others can play off him.
"Andy and Wayne Rooney together would work very well and it would benefit Wayne, who is often carrying England's hopes all on his own.
"It would take the pressure off Wayne, who is still so important to England.
"I'm not going for any of that stuff about Rooney being on the way down. Against us I thought he was really good and some of his passing was excellent. He can play anywhere as far as I'm concerned but I do think he works well off a dominant striker.
"Michael Owen always used to say he had his most productive spell when he was up front with Emile Heskey.
"Heskey did not score many goals but Owen got plenty because of him. And the bonus with Andy Carroll is he is a better goalscorer than Heskey."
Meanwhile, Ricardo Vaz Te has praised Carroll, saying: "I call him a beast. He is great in the air. His accuracy is perfect. On the floor as well he can play and hold the ball.
"We need players who are not afraid to play against big teams."