Beckham, the former England skipper who played 115 times for his country - more than any other outfield player - told BBC Sport in an interview filmed in Los Angeles: "Ideally of course we want an English manager leading the England team, simple as that.
"But we haven't had those options in the last few years so we've had a manager that has been successful all over the world in Fabio Capello.
"But going forward, every Englishman would want an English manager."
Beckham also said Wayne Rooney should be selected in the squad for Euro 2012, even though the striker is banned for the first three matches unless the English FA wins the appeal it has made to UEFA, European football's governing body, to get the punishment reduced.
Rooney was suspended by UEFA for hacking Montenegro's Miodrag Dzudovic in last month's Euro 2012 qualifier in Podgorica but Beckham said Rooney should be included in Capello's 23-man list.
"He is such an important player for our country and once we get through those first stages, that's when a player like Wayne Rooney will come into play," said the LA Galaxy midfielder.
"Obviously it's disappointing he's going to miss those games but, if you have a chance of taking a player like Wayne, you have to take him of course."
He also reiterated his desire, even at the age of 36, to be part of the Britain team which will be taking part in the football tournament at the Olympics for the first time since 1960 next year in London.
"All kids think about it," he said, "I might be 36-years-old, but I'm still a kid when it comes to leading my country, so yeah: we all dream about it and think about it: if it happens I would be honoured."
Beckham helped Galaxy reach Major League Soccer's Western Conference final this week, but although his five-year contract with the club ends later this month, he said his future was still undecided.
Asked about a possible move to Paris Saint-Germain, Beckham said he knew they had shown an interest, but nothing had been finalised.
"I personally have not spoken to them yet but obviously there is interest, " he said.
"But there is also interest in me staying here, and interest in me going to certain clubs in the Premiership, and at 36, for people to still have that interest in me is an honour. I am very flattered by that but right now I am a Galaxy player."
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