He said: "It does not really matter who the leaders are, as long as we keep them in sight.
"At the moment it is Arsenal up there, so we just need to make sure that we keep hold of them for now. I am sure a time will come this season when they start to find it difficult, especially with all the young players they have in their side.
"There is no secret they are a great side, but I am sure they will be tested at some point. We just have to make sure we are there to capitalise when it happens.
"I am sure that Arsenal, Manchester United and Chelsea will keep winning, so it is up to us to prove we can stay with them. It would be really exciting if it is a four-horse race with 10 games to go."
Carragher continued: "Christmas is always a crucial time of the season. You can look at this period almost as a separate group of games in that sense.
"From these three games we would always say that seven points would be fine, but nine would be excellent. That would make a massive difference heading into the new year, hopefully we can them be a lot close to Arsenal by then."