Beckham announced his decision to retire on Thursday afternoon after speculation mounted that he could extend his stay at Paris Saint-Germain.
But the England manager still thinks that he has a part to play in the game beyond his retirement.
"I wish him well in the future whatever he chooses to do and I personally hope that will be in football," Hodgson told Sky Sports News.
"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."
Hodgson was speaking after announcing his latest England squad for the friendly international against Republic of Ireland.