Terry is scheduled to stand trial on allegations of racially abusing Ferdinand's brother Anton – charges with Terry denies – in July, and at present it remains unclear how the long-time international colleagues feel about possibly playing alongside each other at this summer's European Championships.
Hodgson said he would speak to the Chelsea captain Terry and Manchester United centre-back Ferdinand at the earliest opportunity, in order to work out whether the differences between them can be worked around.
"I'll get in touch with John and Rio to speak with them, hopefully face to face, and find out where they are in this situation," said Hodgson.
Terry will not be getting the captain's armband back after the decision to strip him of it led directly to Capello's exit.
"It's a decision that's made by the executive board of the FA," said Hodgson. "I have no reason to comment on it or discuss it. But it's one I am fully prepared to accept."
On Tuesday, the day of his official unveiling as the new boss, Hodgson set his team the minimum target of reaching the Euro 2012 quarter-finals this summer.
Hodgson signed a four-year contract that will take him to the European Championships in France, but events in Poland and Ukraine this summer are uppermost in his mind at present.
"The European Championships are tough, with 16 teams who are among the best in the world, not only Europe, and our group is one of the hardest," he said. "But I'd be bitterly disappointed if we didn't get out the group."
He added: "One is tempted to say, because it's England, that success is only reaching the latter stages, or even the only success is winning. But I'd like people to cut us a bit of slack because the resignation of Fabio Capello has made the situation somewhat different."
Hodgson was only offered the job on Sunday afternoon and was understandably reluctant to get into specifics about the likely make-up of his squad.
He did confirm that there would be no expanded squad taken to a planned training camp in Spain, something he found easier to deal with during his successful stint with Switzerland.
However, the potential for injuries in those last-day fixtures mean he will spend little time thinking about exactly who he will require for pre-tournament friendlies against Norway and Belgium.