Ferdinand pulled out of England's away Group H matches against San Marino on Friday and Montenegro four days later, saying he needed to follow a strict fitness plan laid down by his club.
The Manchester United player was widely criticised on Thursday when it emerged he had agreed to fly to Qatar, a lengthy long-haul journey, in order to work as a TV pundit for the San Marino match for broadcaster al-Jazeera.
Hodgson, who had selected the 81-cap centre-back for the first time since becoming manager last May, was reluctant to criticise the player but non-committal about his future.
"I don't have any serious thoughts on it. I was disappointed when he didn't accept the invitation so what he does now is his business and the club's business and as far as I'm concerned I'm happy with the squad and that's my focus," Hodgson told reporters on Thursday.
When pressed on whether this could be the end of Ferdinand's international career, he said: "I think we should just wait and see.
"It depends on how his injury impacts on England, so we'll wait and see, but I'm happy with the squad we've got."
Ferdinand launched a vigorous defence of himself on Twitter, saying the trip to Qatar was nothing out of the ordinary.
"Flown out for some pre-planned downtime... with a bit of punditry thrown in for a game I would have watched anyway," he said on Twitter.
"No different from what I done on the last 10-day international break... thank you guys."
Hodgson is facing a central defensive shortage for the double header having lost the services of Gary Cahill, Phil Jagielka and Michael Dawson, prompting suggestions he might turn to midfielder Michael Carrick to fill in.
"We have got four top players here, they are playing at top clubs and have a lot of experience," Hodgson said.
"I would be loathe to start using playing like Michael Carrick who has been selected for his prowess in central midfield and it would be harsh on the four central defenders who are here."
