Current No. 1 David de Gea failed to impress in Sunday’s 2-1 win at West Brom and in the Community Shield win over Manchester City.
Lindegaard said: “I’m not scared about being No.1 at Man United. That is why I came here – to play and be the best.
“It doesn’t matter who cost what, the manager will make his decision.
“I’m proud to have created a debate over the goalkeeper position. But I want more than that.
“I have no fear and I have belief in my own ability to perform at this level, otherwise I wouldn’t be here. I want more than making it a difficult decision for the boss. I want to play regularly.”
“We’re very similar, but I’m sure I can learn a thing or two from him, just as he probably can learn a thing or two from me,” he said of De Gea.
“He’s a good kid and he’s very easy to work with. There’s a good atmosphere in training and the competition between us is very healthy.”
Lindegaard impressed during United’s pre-season in America this summer.
He added: “Six months ago, I couldn’t have dreamt of a better scenario than this. I knew this pre-season would be incredibly important to my Manchester United career, the trip to the US was the real test.
“I was pleased with my performances and I have a feeling I’ve fulfilled both mine and everyone else’s expectations.
“My pre-season has been close to perfection. That gives me great belief in myself and my abilities and I’m very optimistic going into the new season.”