The Hammers beat Wolves to progress to the fourth round on Saturday.
The Hammers are currently sixth in the table just after the halfway stage of the season, just four points away from Tottenham in fourth.
They started their FA Cup journey on Saturday, beating Championship side Wolves 1-0 at Upton Park to progress to the fourth round.
It is not a competition they have done well in in recent years, but Reid says they can target a long run this year with their league position so strong.
“We said beforehand that we wanted to go through and you know they're a tough team,” he told whufc.com.
“We haven't done so well in the tournament over the last couple of years, but I think our league position allows us to have a bit more of a go and we intend to.”
“We're in it for the long haul and we'll try our best.”
Given West Ham’s strength in depth this season, there is no reason they can’t challenge for the FA Cup and a Champions League place this season.
Despite a number of injuries to big stars over the busy Christmas period, Slaven Bilic’s side coped well and continued to pick up points with a depleted squad.
With several of those stars having now returned or set to return, there is nothing to stop the Hammers competing on two fronts in the second half of the campaign.