United are halfway through Van Gaal's debut season as manager and a nine-match unbeaten run has helped them rise to third in the Premier League table.
One of United's recent victories came against Stoke at Old Trafford at the beginning of December, Marouane Fellaini and Juan Mata scoring either side of Steven N'Zonzi's equaliser.
However, Van Gaal's men had to withstand late pressure from Mark Hughes' side on that occasion, with goalkeeper David de Gea pulling off a string of impressive saves.
Van Gaal is confident United can continue to adapt to his methods as the Premier League welcomes in 2015, but is wary of the challenge Stoke will pose at the Britannia Stadium.
"I remember that match when we played Stoke at home and we were very weak at the end," he said.
"Maybe you remember what I said at the time that I have to look in the balance of my team and the balance of my team was not as good as it is now.
"I think everyone can see that we are improving every week in spite of a lot of injuries, and that's because of the philosophy, but we can improve more when we have all the players available.
"When I say every week we are improving, then we have to show that against Stoke City."
United have welcomed back defensive trio Luke Shaw, Chris Smalling and Rafael back from injury over the Christmas period.
Van Gaal's options have been further boosted by the return to training of Ander Herrera and Adnan Januzaj from an ankle injury and illness respectively, but they appear unlikely to feature this week.
Angel di Maria (pelvis) and Fellaini (rib) are also expected to miss out once more, while Marcos Rojo (thigh) and Daley Blind (knee) remain absent.
Stoke may have lost to United this month, but they can take confidence from a 2-1 win in last season's corresponding fixture in February - their only Premier League win over United.
Manager Hughes - who enjoyed two spells as a player at Old Trafford - has also seen his team beat the likes of Manchester City, Arsenal and Tottenham this term and is sure Stoke can be a threat on New Year's Day.
"We know that we can go up against the top teams and give them a game," he said. "We beat Chelsea last year, ran United close at their place and beat them here last season, we've beaten Arsenal too.
"We're looking up. We're just out of the top 10 but we're in shouting distance."
Stoke, whose 2-0 win over West Brom on Sunday secured back-to-back league wins for the first time this season, could be without in-form forward Bojan Krkic, who has gone for a scan on a hamstring injury, but Jonathan Walters is fit to play despite a recent illness.
Hughes is also likely to once more be without the trio of Steve Sidwell (knee), Phil Bardsley (ankle) and Stephen Ireland (knee).
