New England have reached four finals but never won, with defeats in 2002, 2005, 2006 and 2007 preventing them from lifting the biggest prize in the American game.
Of those defeats, two - in 2002 and 2005 - came against four-time winners Galaxy.
LA can become the most successful team in the competition's history with victory - DC United have also won four titles - while the Revolution will be desperate to break their MLS Cup hoodoo.
"We're not looking at history right now. We're looking at this as one game," New England coach Jay Heaps said.
"We want to stay focused because it's been our model all year. Every roll of the ball matters and every play matters.
"We've got to focus on this game right now. It would mean a lot to our group [to win]. Right now, we want to do everything to prepare to focus.
"The focus has to be on Sunday's game and preparing for LA Galaxy, and not worry about any of the extra stories that are out there."
New England, who finished second in the Eastern Conference in the regular season, beat Columbus Crew 7-3 on aggregate in their play-off opener, before ending Thierry Henry's New York Red Bulls career with a 4-3 success in the Conference final, despite 18-goal midfielder Lee Nguyen failing to fire across the two legs.
The Galaxy's run through the play-offs saw them comfortably account for Real Salt Lake 5-0, but they had to come from behind to edge Seattle Sounders on away goals and become Western Conference champions.
Seattle led 2-1 on aggregate at half-time of the second leg, but Juninho's 54th-minute goal proved crucial for Bruce Arena's men.
Robbie Keane - who netted 19 times in the regular season for LA - won the MLS MVP this week and looms as a danger man for the Galaxy on Sunday.
Keane, who joined the Galaxy in 2011, beat Obafemi Martins, Nguyen and MLS top scorer Bradley Wright-Phillips for the award.
Veteran forward Landon Donovan, the most decorated United States footballer, will retire from football after Sunday's final and has urged his team-mates to seize their opportunity against a good Revolution side.
Donovan said: "It seems perfect [to be playing at home]. But we are playing a team that I think is the best team in the league over the last 12 months.
"Now we get one game at home to win a championship.
"If anybody had said at the beginning of the year that was the opportunity, we would take it in a heartbeat. We are going to go with everything to win it.
"I really want to go out a champion."
The pair met in regular-season action once this term and how Galaxy would love to replicate their 5-1 thrashing of the Revolution on home turf when they meet again this weekend.
