Lindegaard, 26, joined United from Aalesund for a fee of £3.5 million at the start of January and enjoyed his first run-out for the club when appearing in a behind-closed-doors match against Bury on Monday.
Although the club's current No. 1, Van der Sar, is expected to retire at the end of the season, it has also been rumoured that Lindegaard has been brought in as a possible back-up option for another future signing, with United linked with Atletico Madrid's David de Gea and Schalke's Manuel Neuer.
Tomasz Kuszczak has also said he expects to be made No. 1 when Van der Sar departs, but Lindegaard is certainly not prepared to step aside.
"I want to be the best," Lindegaard told the Manchester Evening News. "I want to be first choice. I am not here because I want to be on the bench. I am not thinking about Edwin's situation. I only focus on things I can do something about and that is me.
"Being No. 1 at United is a goal far out on the horizon. It is not something I think about when I go to sleep at night. The only thing I think about then is tomorrow's training. But it is always there on the horizon that reminds you of where you want to go and what you want to be."
Prior to his arrival at Old Trafford, Lindegaard saw his hero Peter Schmeichel say he was not of the standard required by the club. As an icon of Old Trafford and a fellow Dane, Schmeichel's words have inspired Lindegaard to prove the Treble-winner wrong.
"I was Peter Schmeichel when I was playing in my parent's garden," Lindegaard said. "I was always imagining I was Peter at Old Trafford. He has had a huge impact on my choice of becoming a goalkeeper and supporting United. He has been a big source of inspiration for a long time. I met him during the Liverpool game recently and that was the first time I have ever met him in my whole life and it is very special to meet your idol.
"Peter's words didn't hurt me. It is sad he doesn't have the same admiration for me that I have for him! He is the biggest goalkeeping legend in this club along with Edwin and, of course, you would always want people to believe you are very good and very talented and I am sure he did say I was talented.
"But you also always want to have a nice clap on your shoulder especially from someone like him. But I don't use energy on what Peter believes or thinks about me if it is not positive. I just don't use my energy on anything that is not positive for me and I can use in a positive way.
"On the other hand, it is a very big motivation for me. If someone says you are not good enough and are not going to make it, it is a very big motivation. You are able to surprise people and prove them wrong. Hopefully, Peter will eventually say that he is proud that another Dane has made his way in the world's biggest club. Only time will tell."