A controversial Robbie Brady penalty settled September's meeting at the KC Stadium as West Ham slumped to 16th in the embryonic Premier League table while Hull climbed to seventh.
But the gap between the two has narrowed since then and the hosts can climb above Hull with a victory at Upton Park.
And that would be particularly sweet for Noble, who is eager to exact revenge for their loss in Yorkshire.
"We feel we were on the end of an abysmal decision up there with the penalty that they got," Noble, who had a brief loan spell at Hull in 2006, told the club's official website. "We probably should have won that game, but that's life.
"We managed to get ourselves above them, although they've gone back in front of us at the weekend, and that's the way football goes.
"We want to take the three points."
Sam Allardyce looked to be leading his side comfortably towards top-flight safety when he masterminded four consecutive league wins in February, but March has seen three defeats on the bounce to leave the London club still very much in the relegation shake-up.
