Rio Ferdinand knows De Gea must get through a rapid settling-in process - but Lindegaard wants to challenge the £18million new-boy.
De Gea is the most interesting of Manchester United's three pre-season signings so far.
Having got his fingers badly burned when Peter Schmeichel left in 1999 and gone through a string of failed replacements, Sir Alex Ferguson knew he could not afford the same mistake again when Edwin van der Sar hung up his gloves.
He identified De Gea as a replacement of outstanding promise and the mistake of not signing Petr Cech on age grounds ensured his tender age was ignored in the move from Atletico Madrid.
However, now the 20-year-old has made a belated arrival on United's US tour, Ferdinand acknowledges the hard work must now begin.
"It is not a problem having a new goalkeeper but it is something we have to address straight away," the England defender told Sky Sports.
"He is young. This is the good thing. This is what people are so excited about.
"Across the board, the manager has brought in young, hungry players who have not won anything.
"I came in like that. I know what it is like. Hopefully, those players will have the same attitude."
De Gea's problem is that Lindegaard is equally determined to make his mark.
In the Spain Under-21 international's absence, and with Tomasz Kuszczak left at home ahead of a likely move away from Old Trafford, Lindegaard kept goal for Wednesday's tour opener in Boston.
Ferguson will not be picking De Gea for Wednesday's encounter with Seattle Sounders, which will give the 27-year-old another opportunity to impress.
And as, like De Gea, Lindegaard believes he fits the indentikit Ferguson was looking for as Van der Sar's replacement, he is not willing to concede he will just be a bit-part player.
"In terms of goalkeepers you can definitely see the red line in what the club is doing," he said.
"You can see the type of goalkeeper the club wants. They are aiming for the same kind of goalkeeper as Edwin van der Sar. Good with your feet, tall, agile.
"That is how De Gea is. That is how I play myself."
And, unlike Van der Sar, De Gea as yet does not cast an enormous shadow over the battle for a first-team place.
In completing his United move from Aalesund in January, Lindegaard has the advantage of already completing the acclimatisation process.
And he is not willing to concede he has come to Manchester purely as a bench warmer.
"The manager has said he doesn't care what my name is, what my religion is or how I look," he said.
"He has pointed out if I am good enough, I will get your chance. That is how it is at Manchester United.
"We all start from scratch at the beginning of a new season.
"Edwin was a clear number one. Now he has got his pension and is hopefully enjoying himself in the Bahamas or wherever he is, it is different now.
"I was fortunate in getting to know the team last season.
"The first half year was a learning process. I came from a very little team and into the biggest club in the world.
"Now I have to show I learned those lessons."
Having begun the competitive element of their pre-season work after only a week's training, United's players have decamped in Seattle for seven days ahead of what will be a far more intense end to the tour.
Using the Seattle Seahawks impressive facilities, Sir Alex Ferguson has been presiding over double sessions amid the usual commercial commitments, which yesterday involved an appearance for Ferdinand, Nemanja Vidic and Park Ji-sung at the official away kit launch at Niketown.
All four Under-21 representatives - De Gea, Danny Welbeck, Tom Cleverley and £18million defender Phil Jones - have now arrived, with Javier Hernandez's eagerly-anticipated presence scheduled in another week.
Others are not so lucky, although as yet there has been no official response to suggestions Darren Fletcher is still to make a meaningful appearance at United's Carrington training ground due to fears of a relapse in his recovery from a debilitating virus.
Although Fletcher is largely viewed as a defensive presence, his troubles may bring fresh focus to the presently stalled bid to sign Wesley Sneijder.