Van Gaal feels United played some “sparkling football” in the midweek win over Stoke and another victory at Chelsea on Sunday would reignite their campaign.
His comments come less than a fortnight after a dismal loss to Southampton that saw United and Van Gaal booed at Old Trafford and intensified speculation over his future.
But United got back to winning ways with victory at Derby in the FA Cup and then switched to a more attacking style to brush Stoke aside 3-0.
They are still 10 points behind Barclays Premier League leaders Leicester but Van Gaal claims the gap is not insurmountable.
He said: “I have the feeling that when we shall beat Chelsea - and that is not simple, that is very difficult, since Guus Hiddink has been there they don’t lose any more - I think our competition, our league is starting again. That is very important.
“The competition is not yet finished, not for Manchester United or the other teams. We have the feeling, and that’s because we are winning twice in a row and with sparkling football - with goals and clean sheets, against opponents who were in great form.
“Stoke City played Liverpool off the pitch in the Capital One Cup but they lost on penalties.”
Van Gaal is also hopeful of taking his side to the Europa League final, if his comments on left-back Luke Shaw are anything to go by.
Shaw suffered a double leg break in the Champions League game at PSV Eindhoven in September but has been included in United’s squad for the Europa League in the second half of the season.
Van Gaal said: “He can play the final. That I have said to him.
“That is a goal he has to live for. It is possible, not impossible in my opinion.”
Van Gaal may be expecting a tough test against Hiddink’s side at Stamford Bridge but was unwilling to engage in conversation about his fellow former Dutch national boss at his latest press conference.
The pair are two of Holland’s most successful managers of recent times but are not close.
Asked what his past dealings with Hiddink were like, Van Gaal said: “Professional.”
In the past, Holland international Wesley Sneijder has described Van Gaal as a “tough schoolteacher” and Hiddink as a “friendly uncle”.
Van Gaal was also unwilling to comment on those remarks.
For his part, Chelsea interim boss Guus Hiddink said Louis van Gaal must accept scrutiny as manager of a Manchester United side vying for the title.
“He has to perform, this is normal, as we have to perform here as well,” Hiddink said.
“There is pressure. There was and still is big ambition. They have to cope with that.
“The pressure is on. It’s on everyone.
“But if you have the possibility to go into first position, then pressure is on.”
Hiddink replaced Jose Mourinho at Chelsea in December and declined the opportunity to fully appraise United’s season, suggesting the Blues had enough concerns of their own.
The London side remain in the bottom half of the table entering this weekend’s fixtures.
“I am not going into the ‘problems’ from other clubs as well,” Hiddink added.
“We can talk all morning about Manchester United, but I’m wearing a different colour.
“Every club during a season has some periods where they might worry a bit. We had that as well. I don’t like to go in too much in other people’s kitchen.”
Chelsea are 16 points adrift of Arsenal in fourth, the final Champions League qualifying place.
Hiddink has overseen two wins and five draws in his unbeaten seven-match League run and, with the top four seemingly out of Chelsea’s reach, he hinted the priorities are now the FA Cup and Champions League, where Manchester City and Paris St Germain,are the opposition.
“To get fourth position you need to win, win, win. That’s very, very difficult,” he added.
“The other two legs are FA Cup and Champions League. That’s where we’re aiming.”
Chelsea’s troubles and likely lack of European football - unless they win the Champions League, like in 2012 - could lead to a high player turnover this summer.
Ramires has already left for the Chinese Super League and it was reported Oscar was the subject of a £57m bid from Jiangsu Suning.
“Ramires, we can say he had a great offer. Oscar is just for me, speculation, and we don’t go into that,” Hiddink added.
“We don’t know anything about this.”
Angel Di Maria says he does not want to be reminded of his “sad experience” at Manchester United as he looks to drive Paris St Germain on to domestic and European success.
The 27-year-old arrived at Old Trafford in a much-heralded £59.7m switch from Real Madrid in August 2014, but left for France last summer after 32 appearances in his one season.
And Di Maria has no regrets about his £44m switch to join Laurent Blanc’s squad, who are the runaway leaders of Ligue 1 and face Chelsea for a place in the quarter-finals of the Champions League.
“Manchester United was a sad experience. Things didn’t go as I had hoped.
“I was disappointed and it didn’t help me to rise to the surface,” Di Maria told L’Equipe.
“Honestly, I don’t even remember any more what happened and I don’t want to remember.
“I am happy to be here and that’s the most important thing.”
Di Maria is confident he can continue to impress for PSG, having scored eight goals in Ligue 1 and created many more alongside Swedish striker Zlatan Ibrahimovic and fellow South Amercians Lucas Moura and Edinson Cavani.
“Every day here I feel better and better integrated into the team, the club and the city and that’s reflected in my performances,” he said.
“I know that the two matches to come against Chelsea will determine a lot of things.
“Everyone sees us as the favourites. We don’t see it that way.
“It is Chelsea - they have a quality squad and players that every club in Europe would want to have.”