Allardyce is just one of a number of bosses that have been linked with taking the post when Fabio Capello steps down after next year's European Championships.
Nolan, who has also played under Allardyce at Bolton Wanderers and Newcastle United, has claimed that the 56-year-old should have been handed the role instead of Steve McClaren in 2006.
"No disrespect to Steve McClaren, but when he got the England job I thought Sam should have had it as he was the main candidate then," said Nolan. "I don't know why he didn't get it. He's portrayed as this long-ball, kick-off merchant, but you guys can portray people any way you want.
"If someone wants to portray Sam as a calming influence as a manager, I think they could now. When you see him he's a lot calmer on the sidelines.
"In my opinion, he is still ready for the job and I think he would do a good job if he got that call."
Allardyce and Nolan both joined West Ham during the summer.