The Hammers are currently seventh in the table after a strong start under Slaven Bilic.
The Hammers have enjoyed a fine start to the season under new manager Slaven Bilic and are currently seventh in the table after 15 games.
They are within touching distance of the European places, just three points behind Tottenham Hotspur in fifth and six points behind Manchester United and Manchester City in third and fourth.
With big wins against the likes of Arsenal, City and Liverpool under their belts, the fans are dreaming of a finish high up the table, and Gold says they can finish in the top six.
“We dream of the impossible, we pursue the impossible,” he told Sky Sports.
“I would still say to you that our dream is to finish in the top half of the division. Can we finish in the top six? Yes we can.”
While West Ham’s start puts them in a commanding position to challenge for a top-six place this season, their recent injury crisis is threatening their hopes.
Losing star man Dimitri Payet was the biggest of blows, but also having lost Manuel Lanzini, Victor Moses, Diafra Sakho and Winston Reid for the crucial Christmas period is likely to prove a big blow.
If the Hammers can get over that and still be in the mix, there is every chance they can make the top six and beyond this season.