This season is the last that the Irons will play at the ground that has been their home since 1904, with the club taking up residence in the Olympic Stadium from the start of the next campaign.
Noble is desperate for the club to enjoy further success in the watershed campaign, and when asked on the club's website whether he thought his side had built up some momentum, he replied: "I hope so.
"There's the FA Cup game against Blackburn on Sunday, we've had a few days to rest after the couple of weeks we've had, and our league position allows us to go into the cup game and give everything.
"It would be a fantastic thing for the club to have a run in the FA Cup in the last season at Upton Park."
The Hammers have already gone further in the FA Cup this season than they have in the last three seasons, in all of which they crashed out in the third round, and they have only progressed to the quarter-finals once since losing the 2006 final to Liverpool on penalties.
After this weekend's fifth-round tie, they will turn their attentions back to their push for European football, with the club sitting just one point behind Manchester United in fifth and seven points off a Champions League spot.