Villa manager Martin O'Neill revealed earlier on Wednesday that Young is considering an approach from another club and it is believed that club is Liverpool.
Hodgson, though, would not be drawn when questioned at a press conference ahead of Thursday's clash with FK Rabotnicki.
He spoke at length about the game - his first competitive fixture since taking charge - but appeared agitated when the subject changed to other matters.
When asked about Young and on rumours linking Rodriguez with a return to Espanyol, the 62-year-old said: "They are not playing tomorrow."
Hodgson was also unhappy when asked if reports that Insua's proposed move to Fiorentina had hit a snag were true.
"No information to be given about that," he said.
When another question was asked about the difficulties of trying to sign English players - to comply with new Premier League squad rules - in the current market, Hodgson decided to make a firm point.
He said: "We're changing the subject. I don't think it's right in a room full of Macedonian journalists to be talking about things like homegrown rules and English players.
"I think we should be talking about the game, because that is what interests people.
"The subjects you are bringing up now are subjects for a future press conference.
"It is quite important in these last seven minutes that the questions I try to answer - and I gladly will for the Macedonians - will be about the football match tomorrow and not things like systems of play and future transfer targets or the long-term future of English football."
On the subject of the game Hodgson admitted there was never much chance of him playing the likes of Steven Gerrard and Joe Cole.
Gerrard, Cole and fellow England World Cup players Jamie Carragher and Glen Johnson were among the notable absentees for the third qualifying round first leg against FK Rabotnicki.
Hodgson said: "We were never close to that because they have only been training for four days.
"It would have been folly to try to play 90 minutes' football in an important competition in difficult conditions with players who have only been training for four days.
"We have pressed one or two players into service who were back one or two days earlier than that but in an ideal world we would not have used any of the players that played in the World Cup.
"But, quite frankly, we are not in a strong enough position to do that."
Javier Mascherano and Maxi Rodriguez, who returned to training this week, have also been left out of the squad while Fernando Torres, Jose Reina, Ryan Babel and Dirk Kuyt are still on holiday.
The likes of Diego Cavalieri, Martin Kelly and Jay Spearing are therefore all likely to get an opportunity.
Hodgson said: "All competitions are important to the season.
"It's the first competitive game I have been able to have with the club.
"It would have been nice if the game was played later and we were able to play what we feel is our strongest team but we can't.
"But it is still a very important game and I hope the players we will give the confidence to play in this game and represent Liverpool will be able to do a good job."