Slaven Bilic's men are sixth in the table, and are currently on an impressive run that has seen them lose just once in their last 11 league games. And Noble has reminded the players to remain focused to ensure that they capitalise on their brilliant start, during the second half of the campaign.
"We're sixth in the table, it's our highest league position ever at this stage," he said, as reported by the Star.
"Why would we want to get into this position and waste it? The expectation is there because of the teams we have beaten and the results we've had.
"We went into the Christmas period with players who weren't fit and players who have played no football for us and we came out of it unbeaten."
While the Hammers' current run is undoubtedly impressive, and will give supporters the confidence that they will finish their last season at the Boleyn Ground having achieved one of their best ever finishes in the top flight, Noble will know from painful experience how things can dramatically change.
Last season under Sam Allardyce, West Ham found themselves in the top four at Christmas, but endured a terrible run after the new year which saw them win just three more times in the league, and finish the campaign outside of the top half.
However, victories over Arsenal, Manchester City and Chelsea, as well as a league double over Liverpool has suggested that the squad are in a much better position this time around.
And with the side emerging through the Christmas period largely unscathed, despite a considerable number of injuries, it appears that Bilic's men are in a great position to make sure that they do capitalise on their promising start.