"I've had periods as the first-choice goalkeeper and that is well above my expectations," Lindegaard, who has made 24 starts since joining United in November 2010, told Danish newspaper Jyllands-Posten on Friday.
"But that shouldn't be confused with me being content. Personally, I still haven't achieved my dreams at United.
"I want to be a regular in the team, playing every match and delivering in big games."
Lindegaard was considered as a possible replacement for Edwin van der Sar, who was nearing the end of his career when the Dane joined United, but the arrival of De Gea just seven months later railroaded his plans.
Two layoffs for ankle injuries in 2012 did not help matters and some critics also thought the 28-year-old Lindegaard had been penalised by Sir Alex Ferguson for opting to miss the Premier League derby with champions Manchester City in December to attend the birth of his son.
Lindegaard dismissed that theory and is confident he can prove that he has the credentials to be the top choice keeper.
"In my eyes it is a human right for us men to be there when our children come into the world. Even if it had cost me my place in the team, I would still have chosen to be there for [Lindegaard's partner] Missé and Julian," he said.
"If I had played football when Julian was born, I would have regretted it until the day I die."
Lindegaard's last appearance for Manchester United was in the 1-0 FA Cup victory over West Ham in January, but again De Gea was preferred to him in the fifth round tie against Reading.
But if he wants to keep his place in Morten Olsen's Denmark squad, Lindegaard knows he will have to play regularly at United.
"Morten has always said very clearly that you have to play for your club if you want to play in the national team. For me, playing in the club therefore goes hand in hand with playing in the national team," he said.
"I could of course have prioritised the national team over club football when I joined from Aalesund, I could have chosen a smaller club with guaranteed playing time. But remember that United for me was a lifelong dream come true.
"I feel confident that with playing time for United, I can achieve success with the national team too."
