Ah, a question that vexes the media every time a new England manager must be appointed. (We have similar discussions in Scotland, muted somewhat by the fact that we tend not to care very much. And I daresay other nations have similar considerations.)
Firstly, I should probably note that I have very little doubt that the next England manager will, indeed, by English. Basically, for the FA to go for anyone other than Harry Redknapp, after the failures of the Capello regime, would be too much of a risk - the only reasons I can see this not happening is if Harry doesn't want the job or if Spurs are unreasonable.
However, in general, should the manager of England be English?
Well, as things stand, the answer is "not necessarily". The job of the England manager is to deliver success on the pitch, as reflected in the winning of major trophies. The job of the FA is to find and appoint the person best able to do so. And it would be foolish, under those circumstances, to do anything other than look at all the options.
The perfect candidate for the job would seem to be someone who is English, who has strong communication skills, with excellent man-management and tactical awareness, and with a proven track record of management in several different leagues (ideally including the English and Spanish leagues - currently the two best in the world).
Of these qualities, "being English" is the least valuable. Frankly, they should go get Jose Mourinho.
I'm more or less convinced that the actual answer to the question is "yes, of course the manager of England should be English".
Here's the thing: international football is not about who has the best players, necessarily; it is about who has the best team. And it's really hard to argue that the manager isn't a very large part of that - how can you argue that Alex Ferguson hasn't had a massive impact at Manchester United, or that Martin O'Neill hasn't had a huge impact at Sunderland (even when using the exact same players who were underperforming before)? The manager is hugely important, probably at least as important as any single player.
To that end, I'm inclined to think that the rules should be changed - that the manager (and anyone else with access to the dressing room and/or dugout) should have to follow the same eligibility rules as the players.
But that's a consideration for a slightly different world. As with so many things, the FA should be working to the rules as they are now, and not artificially restricting themselves to only English managers if better candidates are available.