The Reds sit second in the Premier League table after Sunday's 3-0 win at Manchester United and many pundits are predicting that they can finally end their 24-year wait for a top-flight title over the next few months.
However, Marsh has attempted to play down the rising expectation levels and insists the club's main aim remains to just get back into the Champions League for next season.
"We haven't achieved anything yet," he told the Liverpool Echo. "We have nine games to go and are in the Champions League places.
"It has been well documented that we started the season wanting to finish in the top four and we are in with a shout of that. Anything more than a top-four finish would be a bonus."
He added: "We are taking each game as it comes and just trying to win every game. We have nine games left and are trying to get as many points as we can and see where that takes us. Our goals haven't changed since the start of the season."
Liverpool go to relegation-threatened Cardiff on Saturday before hosting struggling Sunderland next Wednesday as they look to maintain their recent fine form.