Ferdinand and the Three Lions boss has still not spoken in person but indirect contact has been made over comments what a self-conscious Hodgson admitted could be perceived as an insult.
The England manager was on the London Underground heading to the Emirates Stadium on Wednesday when he told some fellow passengers that Ferdinand would not be picked for the squad to face San Marino and Poland.
"If Rio is still interested after what he might regard as an insult - it wasn't intended as such - and if he doesn't turn his back on us, then I'm not going to turn my back on him," the Telegraph quoted Hodgson, as saying.
"I'm definitely not closing the door on Rio. I'll try and reach him because he deserves an apology from me. To find out he's been excluded in that way, I'm disappointed with. I respect the man and I respect the player," he added.
"I'm very disappointed that my travelling on the Tube and apparently suggesting Rio's career is over to a passing punter has been recorded as it has. All I remember was that I was talking to quite a lot of people on the Tube and one guy said, 'Is Rio in the next squad?' and I might have said: 'I don't think so'. It's a mistake and I need to apologise for that. I have no one to blame but myself," he said. (ANI )