Neill says he is rooting for Hodgson, who he has been close to for more than 30 years.
"Roy has made a very good start to his England career," Neill told the Official Arsenal Magazine. "He is a very old pal of mine, and an honorary Gooner!
"When he started out with [coach] Bob Houghton in Sweden, Roy wrote to me asking if he could come and spend some time at the Arsenal training ground. I was always willing to allow young coaches to come to see how we work.
"Also, I always felt we could learn something from them too because we were open to new ideas.
"He came along and immediately I liked him. It is a friendship that has lasted more than 30 years."