There are a number of reasons, the main one being that he is Scottish.
The FA would never ask a Scot to be England manager, and I am not sure a Scot would take the England job.
But any England manager has also to be "good" with the press, and you may not be aware of this, but Sir Alex is very "bad" with the press.
He gives plenty of interviews, but still refuses to talk to the BBC because of their critisism of his son's business dealings (you never see him on Match of the Day for example).
He has also refused to talk to MUTV (Man Utd TV - their own TV station) in the past because of things they have said)
He can also be very "rude" to the press and at the end of interviews he will say things like "now go away and write your sh1te"
No arguing that he is a great manager, but he has not got the "tact" to be an international manager (the same reason Brian Clough never got it, and also why Mourinho will never be offered it)