The 24-year-old, who travelled with the Three Lions to the European Championships last summer, has not featured for his country since coming on as a substitute in England's 5-0 win over San Marino in October in a World Cup qualifier.
"Roy would be scared to do it because of the reaction he'd get," Sky Sports News quotes Allardyce as saying. "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."
Carroll's club future remains uncertain as he is due to finish his loan spell at West Ham from Liverpool at the end of the season.