The pair have both been the subject of speculation this summer following the Reds' failure to qualify for the Champions League and the departure of manager Rafael Benitez.
The 32-year-old told talkSPORT: "I think there is a lot of talk about this but the people who say these things, a lot of them are doing this to create a bit of pressure around the club.
"I don't think anyone knows these people personally to come out and say that.
"I am sure they will still be involved at the club next season and if they are the aim for the club will be to get back into the Champions League."
Carragher added: "We didn't just miss out, we finished seventh. That is a big disappointment.
"If we could get back in there that would be a great achievement for the club and the manager.
"It is going to be a tough season but if we keep the players we have got and get back to where we were a few years ago I am sure we will give everyone a run for their money."
Carragher is looking forward to working with veteran boss Hodgson, who led Fulham to the Europa League final last season.
"I think it is a great appointment by the club," he said. "I am sure we can move on from this and it will go well."