Beckham, 38, will stop playing at the end of the season, having clinched the French league title with Paris St Germain.
The midfielder has 115 England caps and was part of Fabio Capello's coaching staff at the 2010 World Cup, and Hodgson hopes Beckham will continue to have an influence in the game.
Hodgson told Sky Sports News: "I wish him well in the future whatever he chooses to do and I personally hope that will be in football.
"David is a man of many talents and a lot of people now will be wanting him for different jobs and roles, some of which could take him away from us in football.
"But I'm rather hoping we'll be able to keep him in football because we can really benefit from his experience, we can really benefit from his charisma and we certainly benefit from the magnificent past he has had as a football player."
Hodgson also revealed that Beckham, despite not being involved as an international player under Hodgson, had been in contact with him to wish the side well.
He added: "In David Beckham, England have a very big fan and a very great supporter."
Football Association chairman David Bernstein paid tribute to Beckham and said efforts would be made to keep him associated with English football.
Bernstein said: "In the week following Sir Alex Ferguson retiring which came as a bit of a shock now we have the iconic David Beckham coming out of the game.
"It's unexpected even though he is getting to mature years for a footballer.
"He is an iconic figure in the game, and produced wonderful performances for his clubs, particularly Manchester United.
"When you look at his playing and work for England, no one would ever accuse him of being unpatriotic and not giving everything for his country.
"He is a real loss to the game and I am sure the FA will want to embrace him and to get him closely associated with the organisation.
"I would personally wish him every luck and success - he will be quite a loss to the game."